On self-dual negacirculant codes of index two and four View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2018-11

AUTHORS

Minjia Shi, Liqin Qian, Patrick Solé

ABSTRACT

We study the asymptotic performance of quasi-twisted codes viewed as modules in the ring R=Fq[x]/⟨xn+1⟩, when they are self-dual and of length 2n or 4n. In particular, in order for the decomposition to be amenable to analysis, we study factorizations of xn+1 over Fq, with n twice an odd prime, containing only three irreducible factors, all self-reciprocal. We give arithmetic conditions bearing on n and q for this to happen. Given a fixed q, we show these conditions are met for infinitely many n’s, provided a refinement of Artin primitive root conjecture holds. This number theory conjecture is known to hold under generalized Riemann hypothesis (GRH). We derive a modified Varshamov–Gilbert bound on the relative distance of the codes considered, building on exact enumeration results for given n and q. More... »

PAGES

2485-2494

References to SciGraph publications

  • 2007-08. Extremal Ternary Self-Dual Codes Constructed from Negacirculant Matrices in GRAPHS AND COMBINATORICS
  • 1993-06. Explicit factorization of + 1 overFp with primep≡3 mod 4 in APPLICABLE ALGEBRA IN ENGINEERING, COMMUNICATION AND COMPUTING
  • 2018-07. Good integers and some applications in coding theory in CRYPTOGRAPHY AND COMMUNICATIONS
  • Identifiers

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    http://scigraph.springernature.com/pub.10.1007/s10623-017-0455-0

    DOI

    http://dx.doi.org/10.1007/s10623-017-0455-0

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