Research on N-weight code on finite ring and its application


Ontology type: schema:MonetaryGrant     


Grant Info

YEARS

2017-2020

FUNDING AMOUNT

630000.0 CNY

ABSTRACT

Codes with weight N(≥2) and relative weight N(≥1) over finite rings can be used to construct optimal codes and secret sharing schemes. Therefore these codes have been actively pursued in the coding theory and cryptography. In this project, we study N-weight and relative N-weight codes over finite rings, focusing on their applications to coding theories and cryptography as well. Firstly, by studying the structures of N-weight linear codes over finite rings, this project is devoted to constructing some classes of linear codes or nonlinear codes over finite fields, which can arrive at the Plotkin bound and Griesmer bound. The project also constructs projective 2-weight cyclic codes over finite rings and generates strongly regular graphs by using projective 2-weight codes over finite rings. Moreover, this project constructs new linear codes or non-linear codes by applying N(≥2)-generator generalized quasi-twisted codes and 2-weight codes over finite rings and finite fields. Finally,this project determines the access structures of secret sharing schemes by applying 2-weight codes over finite rings, and constructs several types of new relative N-weight codes over finite rings and finite fields which are then used in the wire-tap channel of type II and the.construction of secret sharing schemes. This project enriches error-correcting theory and guarantees reliability of information transmission in theory. Thorough study of topics in this project is of fundamental importance to promote the development of information technology and national economy. More... »

Related SciGraph Publications

  • 2021-11-29. On the structure of 1-generator quasi-polycyclic codes over finite chain rings in JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
  • 2021-10-30. LCD and ACD codes over a noncommutative non-unital ring with four elements in CRYPTOGRAPHY AND COMMUNICATIONS
  • 2021-10-29. ZpZp2-linear codes: rank and kernel in DESIGNS, CODES AND CRYPTOGRAPHY
  • 2021-10-28. Self-orthogonal codes over a non-unital ring and combinatorial matrices in DESIGNS, CODES AND CRYPTOGRAPHY
  • 2021-08-31. Quadratic residue codes, rank three groups and PBIBDs in DESIGNS, CODES AND CRYPTOGRAPHY
  • 2021-08-27. On Z2Z4-additive polycyclic codes and their Gray images in DESIGNS, CODES AND CRYPTOGRAPHY
  • 2021-07-19. New classes of binary few weight codes from trace codes over a chain ring in JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
  • 2021-06-04. Several classes of asymptotically good quasi-twisted codes with a low index in JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
  • 2021-05-31. Designs in Finite Metric Spaces: A Probabilistic Approach in GRAPHS AND COMBINATORICS
  • 2021-03-30. Strongly regular graphs from reducible cyclic codes in JOURNAL OF ALGEBRAIC COMBINATORICS
  • 2020-09-20. Construction of isodual codes from polycirculant matrices in DESIGNS, CODES AND CRYPTOGRAPHY
  • 2020-09-12. Two families of two-weight codes over Z4 in DESIGNS, CODES AND CRYPTOGRAPHY
  • 2020-02-04. On the number of resolvable Steiner triple systems of small 3-rank in DESIGNS, CODES AND CRYPTOGRAPHY
  • 2019-08-14. One-weight and two-weight ℤ2ℤ2[u,v]-additive codes in CRYPTOGRAPHY AND COMMUNICATIONS
  • 2019-06-14. Repeated-Root Constacyclic Codes of Length kℓps in BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY
  • 2019-03-27. On self-dual and LCD double circulant and double negacirculant codes over Fq+uFq in CRYPTOGRAPHY AND COMMUNICATIONS
  • 2019-03-16. Three-weight codes, triple sum sets, and strongly walk regular graphs in DESIGNS, CODES AND CRYPTOGRAPHY
  • 2019-01-24. A new distance-regular graph of diameter 3 on 1024 vertices in DESIGNS, CODES AND CRYPTOGRAPHY
  • 2018-11-29. Additive perfect codes in Doob graphs in DESIGNS, CODES AND CRYPTOGRAPHY
  • 2018-08-25. Trace codes over Z4, and Boolean functions in DESIGNS, CODES AND CRYPTOGRAPHY
  • 2018-08-13. On self-dual and LCD quasi-twisted codes of index two over a special chain ring in CRYPTOGRAPHY AND COMMUNICATIONS
  • 2018-05-05. How many weights can a linear code have? in DESIGNS, CODES AND CRYPTOGRAPHY
  • 2018-01-22. On self-dual negacirculant codes of index two and four in DESIGNS, CODES AND CRYPTOGRAPHY
  • 2017-10-28. New Classes of p-Ary Few Weight Codes in BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY
  • 2017-07-18. On two-weight Z2k-codes in DESIGNS, CODES AND CRYPTOGRAPHY
  • 2017-05-11. On codes over Fq+vFq+v2Fq in JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
  • 2017-03-14. Classification and Construction of quaternary self-dual bent functions in CRYPTOGRAPHY AND COMMUNICATIONS
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