有限域上的广义准多项式码
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摘要
文章提出了一类新的码——广义准多项式码,它是多项式码的一种推广.文中首先给出了广义准多项式码的概念及其生成矩阵的结构,然后重点研究了1-生成元的广义准多项式码参数的相关性质,并且基于这些性质构造出了一些最优码.
In this paper,we investigate a new class of codes which called generalized quasi-polycyclic codes(GQPCs).We first introduce the concept and the generator matrix of GQPCs.Next,we mainly consider 1-generator GQPCs and give some results about their parameters.Finally,we obtain some optimal codes based on the results.
In this paper,we investigate a new class of codes which called generalized quasi-polycyclic codes(GQPCs).We first introduce the concept and the generator matrix of GQPCs.Next,we mainly consider 1-generator GQPCs and give some results about their parameters.Finally,we obtain some optimal codes based on the results.
引文
[1]Ding C.Cyclic codes from cyclotomic sequences of order four.Finite Fields and Their Applications,2013,23(96):8-34.
[2]Peterson W W,Weldon E J J.Error Correcting Codes.MIT Press,1961.
[3]Alahmadi A,Dougherty S.On the duality and the direction of polycyclic codes.Advances in Mathematics of Communications,2017,10(4):921-929.
[4]Manabu Matsuoka.θ-polycyclic codes andθ-sequential codes over finite fields.Int.J.Algebra,2011,5(1-4):65-70.
[5]Li S,Xiong M,Ge G.Pseudo-cyclic codes and the construction of quantum MDS codes.IEEE Trans.Inf.Theory,2016,62(4):1703-1710.
[6]Ling S,Sole P.On the algebraic structure of quasi-cyclic codes.I.Finite fields.IEEE Trans.Inf.Theory,2001,47(7):2751-2760.
[7]Siap I,Kulhan N.The structure of generalized quasi cyclic codes.Applied Mathematics E-Notes,2005,5:24-30.
[8]Esmaeili M and Yari S.Generalized quasi-cyclic codes:Structural properties and code construction.Applicable Algebra in Engineering,Communication and Computing, 2009,20(2):159-173.
[9]Cao Y.Structural properties and enumeration of 1-generator generalized quasi-cyclic codes.Kluwer Academic Publishers,2011.
[10]Guneri C,Ozbudak F.Structure and performance of generalized quasicyclic codes.Finite Fields and Their Applications, 2017,47:183-202.
[11]Shi M,Qian L.Good self-dual generalized quasi-cyclic codes exist.Information Processing Letters,2017,118:21-24.
[12]Grassl M.Bounds on the minimum distance of linear codes and quantum codes.Available at:http://www.codetables.de.
[2]Peterson W W,Weldon E J J.Error Correcting Codes.MIT Press,1961.
[3]Alahmadi A,Dougherty S.On the duality and the direction of polycyclic codes.Advances in Mathematics of Communications,2017,10(4):921-929.
[4]Manabu Matsuoka.θ-polycyclic codes andθ-sequential codes over finite fields.Int.J.Algebra,2011,5(1-4):65-70.
[5]Li S,Xiong M,Ge G.Pseudo-cyclic codes and the construction of quantum MDS codes.IEEE Trans.Inf.Theory,2016,62(4):1703-1710.
[6]Ling S,Sole P.On the algebraic structure of quasi-cyclic codes.I.Finite fields.IEEE Trans.Inf.Theory,2001,47(7):2751-2760.
[7]Siap I,Kulhan N.The structure of generalized quasi cyclic codes.Applied Mathematics E-Notes,2005,5:24-30.
[8]Esmaeili M and Yari S.Generalized quasi-cyclic codes:Structural properties and code construction.Applicable Algebra in Engineering,Communication and Computing, 2009,20(2):159-173.
[9]Cao Y.Structural properties and enumeration of 1-generator generalized quasi-cyclic codes.Kluwer Academic Publishers,2011.
[10]Guneri C,Ozbudak F.Structure and performance of generalized quasicyclic codes.Finite Fields and Their Applications, 2017,47:183-202.
[11]Shi M,Qian L.Good self-dual generalized quasi-cyclic codes exist.Information Processing Letters,2017,118:21-24.
[12]Grassl M.Bounds on the minimum distance of linear codes and quantum codes.Available at:http://www.codetables.de.