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Journal of Systems Science & Complexity 2024年第5期37卷 2196-2206页

作者： SHI Minjia XU Li SOLÉ Patrick Key Laboratory of Intelligent Computing and Signal Processing Ministry of EducationSchool of Mathematical SciencesAnhui UniversityHefei 230601China State Key Laboratory of Information Security Institute of Information EngineeringChinese Academy of SciencesBeijing 100093China CNRS University of Aix MarseilleCentrale MarseilleI2MMarseille 13284France

Double Toeplitz(shortly DT)codes are introduced here as a generalization of double circulant *** authors show that such a code is isodual,hence formally self-dual(FSD).FSD codes form a far-reaching generalization of self-dual codes,the most important class of codes of rate ***-dual DT codes are characterized as double circulant or double ***,even binary DT codes are characterized as double *** examples obtained by exhaustive search show that the codes constructed have best-known minimum distance,up to one unit,amongst formally self-dual codes,and sometimes improve on the known *** q=2,the authors find four improvements on the best-known values of the minimum distance of FSD *** F4 an explicit construction of DT codes,based on quadratic residues in a prime field,performs equally *** authors show that DT codes are asymptotically good over ***,the authors construct DT codes arbitrarily close to the asymptotic Varshamov-Gilbert bound for codes of rate one half.

关键词： Double circulant codes double Toeplitz codes isodual codes formally self-dual codes

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Polyadic Cyclic codes over a Non-Chain Ring

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Journal of Computer and Communications 2021年第5期9卷 36-57页

作者： Mokshi Goyal Madhu Raka Centre for Advanced Study in Mathematics Panjab University Chandigarh India

Let f(u) and g(v) be two polynomials of degree k and l respectively, not both linear which split into distinct linear factors over Fq. Let be a finite commutative non-chain ring. In this paper, we study polyadic codes and their extensions over the ring R. We give examples of some polyadic codes which are optimal with respect to Griesmer type bound for rings. A Gray map is defined from which preserves duality. The Gray images of polyadic codes and their extensions over the ring R lead to construction of self-dual, isodual, self-orthogonal and complementary dual (LCD) codes over Fq. Some examples are also given to illustrate this.

关键词： Polyadic codes and Their Extensions Griesmer Bound Gray Map Self-Dual and Self-Orthogonal codes isodual codes LCD codes

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