Let Fq be a finite field with order q and D2n be the dihedral group with 2n elements, and gcd(q, 2n) = 1. In this article, the authors give precise descriptions and enumerations of linear complementary dual(LCD) codes...Let Fq be a finite field with order q and D2n be the dihedral group with 2n elements, and gcd(q, 2n) = 1. In this article, the authors give precise descriptions and enumerations of linear complementary dual(LCD) codes and self-orthogonal codes in the finite dihedral group algebras Fq[D2n]. Some numerical examples are also presented to illustrate the main results.展开更多
Let <i>f</i>(u) and <i>g</i>(v) be two polynomials of degree <i>k</i> and <i>l</i> respectively, not both linear which split into distinct linear factors over F<sub&g...Let <i>f</i>(u) and <i>g</i>(v) be two polynomials of degree <i>k</i> and <i>l</i> respectively, not both linear which split into distinct linear factors over F<sub>q</sub>. Let <img src="Edit_83041428-d8b0-4505-8c3c-5e29f2886159.png" width="160" height="15" alt="" /> be a finite commutative non-chain ring. In this paper, we study polyadic codes and their extensions over the ring <i>R</i>. We give examples of some polyadic codes which are optimal with respect to Griesmer type bound for rings. A Gray map is defined from <img src="Edit_c75f119d-3176-4a71-a36a-354955044c09.png" width="50" height="15" alt="" /> which preserves duality. The Gray images of polyadic codes and their extensions over the ring <i>R</i> lead to construction of self-dual, isodual, self-orthogonal and complementary dual (LCD) codes over F<i><sub>q</sub></i>. Some examples are also given to illustrate this.展开更多
This paper deduces the structure of LCD negacyclic codes over the finite field Fq, where q is an odd prime power. Based on the study of q-cyclotomic cosets modulo 2n, the authors obtain the parameters of LCD negacycli...This paper deduces the structure of LCD negacyclic codes over the finite field Fq, where q is an odd prime power. Based on the study of q-cyclotomic cosets modulo 2n, the authors obtain the parameters of LCD negacyclic codes of lengths n=qt＋1/2,qm-1/2（q-1） and qt·2τ-1/2（q2＋1）respectively. And many optimal codes are given. Moreover, the authors research two special classes of MDS LCD negacyclic codes of length n｜q-1/2 and n｜q＋1/2,respectively.展开更多
In this paper,we characterize the necessary and sufficient conditions for a cyclic code of length n over F_p+ vF_p to be an LCD code,where p is an odd prime.
Recently,linear complementary dual(LCD)codes have garnered substantial interest within coding theory research due to their diverse applications and favorable attributes.This paper directs its attention to the construc...Recently,linear complementary dual(LCD)codes have garnered substantial interest within coding theory research due to their diverse applications and favorable attributes.This paper directs its attention to the construction of binary and ternary LCD codes leveraging curiosity-driven reinforcement learning(RL).By establishing reward and devising well-reasoned mappings from actions to states,it aims to facilitate the successful synthesis of binary or ternary LCD codes.Experimental results indicate that LCD codes constructed using RL exhibit slightly superior error-correction performance compared to those conventionally constructed LCD codes and those developed via standard RL methodologies.The paper introduces novel binary and ternary LCD codes with enhanced minimum distance bounds.Finally,it showcases how random network distillation aids agents in exploring beyond local optima,enhancing the overall performance of the models without compromising convergence.展开更多
基金supported by the National Natural Science Foundation of China(Nos.61772015,11971321,12101326)Foundation of Nanjing Institute of Technology(No.CKJB202007)+4 种基金the NUPTSF(No.NY220137)the Guangxi Natural Science Foundation(No.2020GXNSFAA159053)the National Key Research and Development Program of China(No.2018YFA0704703)Foundation of Science and Technology on Information Assurance Laboratory(No.KJ-17-010)the Open Project of Shanghai Key Laboratory of Trustworthy Computing(No.OP202101)。
文摘Let Fq be a finite field with order q and D2n be the dihedral group with 2n elements, and gcd(q, 2n) = 1. In this article, the authors give precise descriptions and enumerations of linear complementary dual(LCD) codes and self-orthogonal codes in the finite dihedral group algebras Fq[D2n]. Some numerical examples are also presented to illustrate the main results.
文摘Let <i>f</i>(u) and <i>g</i>(v) be two polynomials of degree <i>k</i> and <i>l</i> respectively, not both linear which split into distinct linear factors over F<sub>q</sub>. Let <img src="Edit_83041428-d8b0-4505-8c3c-5e29f2886159.png" width="160" height="15" alt="" /> be a finite commutative non-chain ring. In this paper, we study polyadic codes and their extensions over the ring <i>R</i>. We give examples of some polyadic codes which are optimal with respect to Griesmer type bound for rings. A Gray map is defined from <img src="Edit_c75f119d-3176-4a71-a36a-354955044c09.png" width="50" height="15" alt="" /> which preserves duality. The Gray images of polyadic codes and their extensions over the ring <i>R</i> lead to construction of self-dual, isodual, self-orthogonal and complementary dual (LCD) codes over F<i><sub>q</sub></i>. Some examples are also given to illustrate this.
基金supported by the National Natural Science Foundation of China under Grant Nos.61370089,61572168,11501156the Anhui Provincial Natural Science Foundation under Grant No.1508085SQA198
文摘This paper deduces the structure of LCD negacyclic codes over the finite field Fq, where q is an odd prime power. Based on the study of q-cyclotomic cosets modulo 2n, the authors obtain the parameters of LCD negacyclic codes of lengths n=qt＋1/2,qm-1/2（q-1） and qt·2τ-1/2（q2＋1）respectively. And many optimal codes are given. Moreover, the authors research two special classes of MDS LCD negacyclic codes of length n｜q-1/2 and n｜q＋1/2,respectively.
基金Supported by the Science and Technology Development Program of Henan Province in 2016（162102410052） Supported by the Natural Science Foundation from the Educational Department of Henan Province（14B110004, 2013-JSJYYB-063）
文摘In this paper,we characterize the necessary and sufficient conditions for a cyclic code of length n over F_p+ vF_p to be an LCD code,where p is an odd prime.
基金supported by the National Natural Science Foundation of China under Grant Nos.62372247 and 12441103the open research fund of National Mobile Communications Research Laboratory,Southeast University under Grant No.2025D01the Open Project of Guangxi Provincial Key Laboratory under Grant No.MIMS22-01。
文摘Recently,linear complementary dual(LCD)codes have garnered substantial interest within coding theory research due to their diverse applications and favorable attributes.This paper directs its attention to the construction of binary and ternary LCD codes leveraging curiosity-driven reinforcement learning(RL).By establishing reward and devising well-reasoned mappings from actions to states,it aims to facilitate the successful synthesis of binary or ternary LCD codes.Experimental results indicate that LCD codes constructed using RL exhibit slightly superior error-correction performance compared to those conventionally constructed LCD codes and those developed via standard RL methodologies.The paper introduces novel binary and ternary LCD codes with enhanced minimum distance bounds.Finally,it showcases how random network distillation aids agents in exploring beyond local optima,enhancing the overall performance of the models without compromising convergence.
