Several classes of asymptotically good quasi-twisted codes with a low index View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2021-06-04

AUTHORS

Hongwei Zhu, Minjia Shi

ABSTRACT

The objectives of this paper are to survey and extend results on several classes of asymptotically good quasi-twisted codes over finite field with a low index, namely double circulant codes, double negacirculant codes, four circulant codes and four negacirculant codes. For a given length, we summarize the enumerations of the self-dual and LCD codes and supplement some expansion results. The existence of asymptotically good quasi-twisted codes relies on factorizations of special binomials over finite fields; the existence of these factorizations, in turn, with the assumption of Artin primitive root conjecture, or in some cases can be derived unconditionally by using Dickson polynomials. More... »

PAGES

1-18

References to SciGraph publications

  • 1989. On the asymptotic badness of cyclic codes with block-lengths composed from a fixed set of prime factors in APPLIED ALGEBRA, ALGEBRAIC ALGORITHMS AND ERROR-CORRECTING CODES
  • 2017-07-20. On self-dual double circulant codes in DESIGNS, CODES AND CRYPTOGRAPHY
  • 2021-01-25. Self-dual and LCD double circulant and double negacirculant codes over Fq+uFq+vFq in JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
  • 2015. Complementary Dual Codes for Counter-Measures to Side-Channel Attacks in CODING THEORY AND APPLICATIONS
  • 2018-01-22. On self-dual negacirculant codes of index two and four in DESIGNS, CODES AND CRYPTOGRAPHY
  • 2019-06-21. On complementary dual multinegacirculant codes in CRYPTOGRAPHY AND COMMUNICATIONS
  • 2007-08. Extremal Ternary Self-Dual Codes Constructed from Negacirculant Matrices in GRAPHS AND COMBINATORICS
  • 2017-12-14. Statistical properties of side-channel and fault injection attacks using coding theory in CRYPTOGRAPHY AND COMMUNICATIONS
  • 2016-09-29. Galois self-dual constacyclic codes in DESIGNS, CODES AND CRYPTOGRAPHY
  • 2019-03-27. On self-dual and LCD double circulant and double negacirculant codes over Fq+uFq in CRYPTOGRAPHY AND COMMUNICATIONS
  • 2018-02-05. Euclidean and Hermitian LCD MDS codes in DESIGNS, CODES AND CRYPTOGRAPHY
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s12190-021-01564-3

    DOI

    http://dx.doi.org/10.1007/s12190-021-01564-3

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1138609421


    Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
    Incoming Citations Browse incoming citations for this publication using opencitations.net

    JSON-LD is the canonical representation for SciGraph data.

    TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

    [
      {
        "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
        "about": [
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Mathematical Sciences", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0101", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Pure Mathematics", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "School of Mathematical Sciences, Anhui University, 230601, Hefei, Anhui, China", 
              "id": "http://www.grid.ac/institutes/grid.252245.6", 
              "name": [
                "Key Laboratory of Intelligent Computing Signal Processing, Ministry of Education, Anhui University, No. 3 Feixi Road, 230039, Hefei, Anhui, China", 
                "School of Mathematical Sciences, Anhui University, 230601, Hefei, Anhui, China"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Zhu", 
            "givenName": "Hongwei", 
            "id": "sg:person.014615732132.58", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014615732132.58"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "School of Mathematical Sciences, Anhui University, 230601, Hefei, Anhui, China", 
              "id": "http://www.grid.ac/institutes/grid.252245.6", 
              "name": [
                "Key Laboratory of Intelligent Computing Signal Processing, Ministry of Education, Anhui University, No. 3 Feixi Road, 230039, Hefei, Anhui, China", 
                "School of Mathematical Sciences, Anhui University, 230601, Hefei, Anhui, China"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Shi", 
            "givenName": "Minjia", 
            "id": "sg:person.012012432235.16", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012012432235.16"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1007/s12095-019-00364-8", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1117403599", 
              "https://doi.org/10.1007/s12095-019-00364-8"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s10623-017-0455-0", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1100556533", 
              "https://doi.org/10.1007/s10623-017-0455-0"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s12095-019-00363-9", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1113044795", 
              "https://doi.org/10.1007/s12095-019-00363-9"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s10623-016-0282-8", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1028172314", 
              "https://doi.org/10.1007/s10623-016-0282-8"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s10623-018-0463-8", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1100823192", 
              "https://doi.org/10.1007/s10623-018-0463-8"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/3-540-51083-4_56", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1011807516", 
              "https://doi.org/10.1007/3-540-51083-4_56"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s10623-017-0393-x", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1090832475", 
              "https://doi.org/10.1007/s10623-017-0393-x"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s12095-017-0271-4", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1099693395", 
              "https://doi.org/10.1007/s12095-017-0271-4"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s12190-021-01499-9", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1134857547", 
              "https://doi.org/10.1007/s12190-021-01499-9"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00373-007-0731-2", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1017013959", 
              "https://doi.org/10.1007/s00373-007-0731-2"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-319-17296-5_9", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1006427136", 
              "https://doi.org/10.1007/978-3-319-17296-5_9"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2021-06-04", 
        "datePublishedReg": "2021-06-04", 
        "description": "The objectives of this paper are to survey and extend results on several classes of asymptotically good quasi-twisted codes over finite field with a low index, namely double circulant codes, double negacirculant codes, four circulant codes and four negacirculant codes. For a given length, we summarize the enumerations of the self-dual and LCD codes and supplement some expansion results. The existence of asymptotically good quasi-twisted codes relies on factorizations of special binomials over finite fields; the existence of these factorizations, in turn, with the assumption of Artin primitive root conjecture, or in some cases can be derived unconditionally by using Dickson polynomials.", 
        "genre": "article", 
        "id": "sg:pub.10.1007/s12190-021-01564-3", 
        "inLanguage": "en", 
        "isAccessibleForFree": false, 
        "isFundedItemOf": [
          {
            "id": "sg:grant.8306127", 
            "type": "MonetaryGrant"
          }
        ], 
        "isPartOf": [
          {
            "id": "sg:journal.1136398", 
            "issn": [
              "1598-5865", 
              "1865-2085"
            ], 
            "name": "Journal of Applied Mathematics and Computing", 
            "publisher": "Springer Nature", 
            "type": "Periodical"
          }
        ], 
        "keywords": [
          "quasi-twisted codes", 
          "finite field", 
          "Artin's primitive root conjecture", 
          "circulant codes", 
          "double circulant codes", 
          "LCD codes", 
          "Dickson polynomials", 
          "factorization", 
          "expansion results", 
          "existence", 
          "polynomials", 
          "class", 
          "conjecture", 
          "field", 
          "code", 
          "binomial", 
          "assumption", 
          "enumeration", 
          "results", 
          "low index", 
          "cases", 
          "length", 
          "objective", 
          "index", 
          "turn", 
          "paper", 
          "good quasi-twisted codes", 
          "double negacirculant codes", 
          "negacirculant codes", 
          "special binomials", 
          "primitive root conjecture", 
          "root conjecture"
        ], 
        "name": "Several classes of asymptotically good quasi-twisted codes with a low index", 
        "pagination": "1-18", 
        "productId": [
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1138609421"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/s12190-021-01564-3"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/s12190-021-01564-3", 
          "https://app.dimensions.ai/details/publication/pub.1138609421"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2022-01-01T19:01", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-springernature-scigraph/baseset/20220101/entities/gbq_results/article/article_903.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "https://doi.org/10.1007/s12190-021-01564-3"
      }
    ]
     

    Download the RDF metadata as:  json-ld nt turtle xml License info

    HOW TO GET THIS DATA PROGRAMMATICALLY:

    JSON-LD is a popular format for linked data which is fully compatible with JSON.

    curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/s12190-021-01564-3'

    N-Triples is a line-based linked data format ideal for batch operations.

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/s12190-021-01564-3'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s12190-021-01564-3'

    RDF/XML is a standard XML format for linked data.

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s12190-021-01564-3'


     

    This table displays all metadata directly associated to this object as RDF triples.

    138 TRIPLES      22 PREDICATES      66 URIs      47 LITERALS      4 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/s12190-021-01564-3 schema:about anzsrc-for:01
    2 anzsrc-for:0101
    3 schema:author N67e08875b20a4bb8bfdfb1a86646077a
    4 schema:citation sg:pub.10.1007/3-540-51083-4_56
    5 sg:pub.10.1007/978-3-319-17296-5_9
    6 sg:pub.10.1007/s00373-007-0731-2
    7 sg:pub.10.1007/s10623-016-0282-8
    8 sg:pub.10.1007/s10623-017-0393-x
    9 sg:pub.10.1007/s10623-017-0455-0
    10 sg:pub.10.1007/s10623-018-0463-8
    11 sg:pub.10.1007/s12095-017-0271-4
    12 sg:pub.10.1007/s12095-019-00363-9
    13 sg:pub.10.1007/s12095-019-00364-8
    14 sg:pub.10.1007/s12190-021-01499-9
    15 schema:datePublished 2021-06-04
    16 schema:datePublishedReg 2021-06-04
    17 schema:description The objectives of this paper are to survey and extend results on several classes of asymptotically good quasi-twisted codes over finite field with a low index, namely double circulant codes, double negacirculant codes, four circulant codes and four negacirculant codes. For a given length, we summarize the enumerations of the self-dual and LCD codes and supplement some expansion results. The existence of asymptotically good quasi-twisted codes relies on factorizations of special binomials over finite fields; the existence of these factorizations, in turn, with the assumption of Artin primitive root conjecture, or in some cases can be derived unconditionally by using Dickson polynomials.
    18 schema:genre article
    19 schema:inLanguage en
    20 schema:isAccessibleForFree false
    21 schema:isPartOf sg:journal.1136398
    22 schema:keywords Artin's primitive root conjecture
    23 Dickson polynomials
    24 LCD codes
    25 assumption
    26 binomial
    27 cases
    28 circulant codes
    29 class
    30 code
    31 conjecture
    32 double circulant codes
    33 double negacirculant codes
    34 enumeration
    35 existence
    36 expansion results
    37 factorization
    38 field
    39 finite field
    40 good quasi-twisted codes
    41 index
    42 length
    43 low index
    44 negacirculant codes
    45 objective
    46 paper
    47 polynomials
    48 primitive root conjecture
    49 quasi-twisted codes
    50 results
    51 root conjecture
    52 special binomials
    53 turn
    54 schema:name Several classes of asymptotically good quasi-twisted codes with a low index
    55 schema:pagination 1-18
    56 schema:productId Na16890a4e6124efcb7481f7e1af872c5
    57 Na1692048d21b4fb4b91a191d6629d3b7
    58 schema:sameAs https://app.dimensions.ai/details/publication/pub.1138609421
    59 https://doi.org/10.1007/s12190-021-01564-3
    60 schema:sdDatePublished 2022-01-01T19:01
    61 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    62 schema:sdPublisher N881d973807564ca98dcc142719a6f7e3
    63 schema:url https://doi.org/10.1007/s12190-021-01564-3
    64 sgo:license sg:explorer/license/
    65 sgo:sdDataset articles
    66 rdf:type schema:ScholarlyArticle
    67 N5a5f933c4a5c4f8ab8968a29b2df2e64 rdf:first sg:person.012012432235.16
    68 rdf:rest rdf:nil
    69 N67e08875b20a4bb8bfdfb1a86646077a rdf:first sg:person.014615732132.58
    70 rdf:rest N5a5f933c4a5c4f8ab8968a29b2df2e64
    71 N881d973807564ca98dcc142719a6f7e3 schema:name Springer Nature - SN SciGraph project
    72 rdf:type schema:Organization
    73 Na16890a4e6124efcb7481f7e1af872c5 schema:name dimensions_id
    74 schema:value pub.1138609421
    75 rdf:type schema:PropertyValue
    76 Na1692048d21b4fb4b91a191d6629d3b7 schema:name doi
    77 schema:value 10.1007/s12190-021-01564-3
    78 rdf:type schema:PropertyValue
    79 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
    80 schema:name Mathematical Sciences
    81 rdf:type schema:DefinedTerm
    82 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
    83 schema:name Pure Mathematics
    84 rdf:type schema:DefinedTerm
    85 sg:grant.8306127 http://pending.schema.org/fundedItem sg:pub.10.1007/s12190-021-01564-3
    86 rdf:type schema:MonetaryGrant
    87 sg:journal.1136398 schema:issn 1598-5865
    88 1865-2085
    89 schema:name Journal of Applied Mathematics and Computing
    90 schema:publisher Springer Nature
    91 rdf:type schema:Periodical
    92 sg:person.012012432235.16 schema:affiliation grid-institutes:grid.252245.6
    93 schema:familyName Shi
    94 schema:givenName Minjia
    95 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012012432235.16
    96 rdf:type schema:Person
    97 sg:person.014615732132.58 schema:affiliation grid-institutes:grid.252245.6
    98 schema:familyName Zhu
    99 schema:givenName Hongwei
    100 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014615732132.58
    101 rdf:type schema:Person
    102 sg:pub.10.1007/3-540-51083-4_56 schema:sameAs https://app.dimensions.ai/details/publication/pub.1011807516
    103 https://doi.org/10.1007/3-540-51083-4_56
    104 rdf:type schema:CreativeWork
    105 sg:pub.10.1007/978-3-319-17296-5_9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1006427136
    106 https://doi.org/10.1007/978-3-319-17296-5_9
    107 rdf:type schema:CreativeWork
    108 sg:pub.10.1007/s00373-007-0731-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1017013959
    109 https://doi.org/10.1007/s00373-007-0731-2
    110 rdf:type schema:CreativeWork
    111 sg:pub.10.1007/s10623-016-0282-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1028172314
    112 https://doi.org/10.1007/s10623-016-0282-8
    113 rdf:type schema:CreativeWork
    114 sg:pub.10.1007/s10623-017-0393-x schema:sameAs https://app.dimensions.ai/details/publication/pub.1090832475
    115 https://doi.org/10.1007/s10623-017-0393-x
    116 rdf:type schema:CreativeWork
    117 sg:pub.10.1007/s10623-017-0455-0 schema:sameAs https://app.dimensions.ai/details/publication/pub.1100556533
    118 https://doi.org/10.1007/s10623-017-0455-0
    119 rdf:type schema:CreativeWork
    120 sg:pub.10.1007/s10623-018-0463-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1100823192
    121 https://doi.org/10.1007/s10623-018-0463-8
    122 rdf:type schema:CreativeWork
    123 sg:pub.10.1007/s12095-017-0271-4 schema:sameAs https://app.dimensions.ai/details/publication/pub.1099693395
    124 https://doi.org/10.1007/s12095-017-0271-4
    125 rdf:type schema:CreativeWork
    126 sg:pub.10.1007/s12095-019-00363-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1113044795
    127 https://doi.org/10.1007/s12095-019-00363-9
    128 rdf:type schema:CreativeWork
    129 sg:pub.10.1007/s12095-019-00364-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1117403599
    130 https://doi.org/10.1007/s12095-019-00364-8
    131 rdf:type schema:CreativeWork
    132 sg:pub.10.1007/s12190-021-01499-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1134857547
    133 https://doi.org/10.1007/s12190-021-01499-9
    134 rdf:type schema:CreativeWork
    135 grid-institutes:grid.252245.6 schema:alternateName School of Mathematical Sciences, Anhui University, 230601, Hefei, Anhui, China
    136 schema:name Key Laboratory of Intelligent Computing Signal Processing, Ministry of Education, Anhui University, No. 3 Feixi Road, 230039, Hefei, Anhui, China
    137 School of Mathematical Sciences, Anhui University, 230601, Hefei, Anhui, China
    138 rdf:type schema:Organization
     




    Preview window. Press ESC to close (or click here)


    ...