Repeated-root constacyclic codes of length 2ps

Abstract The algebraic structures in term of polynomial generators of all constacyclic codes of length 2 p s over the finite field F p m are established. Among other results, all self-dual negacyclic codes of length 2 p s , where p ≡ 1 ( mod 4 ) (any m), or p ≡ 3 ( mod 4 ) and m is even, are provided. It is also shown the non-existence of self-dual negacyclic codes of length 2 p s , where p ≡ 3 ( mod 4 ) , m is odd, and self-dual cyclic codes of length 2 p s , for any odd prime p.

[1]  Madhu Raka,et al.  Existence of cyclic self-orthogonal codes: A note on a result of Vera Pless , 2012, Adv. Math. Commun..

[2]  Shixin Zhu,et al.  On cyclic self-dual codes , 2008, Applicable Algebra in Engineering, Communication and Computing.

[3]  Sudhir Batra,et al.  Some cyclic codes of length 2pn , 2011, Des. Codes Cryptogr..

[4]  Xiang Yang,et al.  The condition for a cyclic code to have a complementary dual , 1994, Discret. Math..

[5]  Hai Q. Dinh,et al.  On Some Classes of Repeated-root Constacyclic Codes of Length a Power of 2 over Galois Rings , 2010 .

[6]  James L. Massey,et al.  On Repeated-root Cyclic Codes , 1991, IEEE Trans. Inf. Theory.

[7]  Rudolf Lide,et al.  Finite fields , 1983 .

[8]  W. Cary Huffman,et al.  Fundamentals of Error-Correcting Codes , 1975 .

[9]  H. Dinh.  Constacyclic Codes of Length p^s Over Fpm + uFpm , 2010 .

[10]  Nicolas Sendrier,et al.  Linear codes with complementary duals meet the Gilbert-Varshamov bound , 2004, International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings..

[11]  J. Wolfman.  Negacyclic and cyclic codes over Z/sub 4/ , 1999 .

[12]  Chaoping Xing,et al.  On Self-Dual Cyclic Codes Over Finite Fields , 2011, IEEE Transactions on Information Theory.

[13]  Thomas Blackford.  Negacyclic duadic codes , 2008, Finite Fields Their Appl..

[14]  F. MacWilliams,et al.  The Theory of Error-Correcting Codes , 1977 .

[15]  Madhu Raka,et al.  Irreducible cyclic codes of length 2pn , 2007, Ars Comb..

[16]  James L. Massey,et al.  Linear codes with complementary duals , 1992, Discret. Math..

[17]  Sergio R. López-Permouth,et al.  Cyclic and negacyclic codes over finite chain rings , 2004, IEEE Transactions on Information Theory.

[18]  Ron M. Roth,et al.  On cyclic MDS codes of length q over GF(q) , 1986, IEEE Trans. Inf. Theory.

[19]  S. Berman.  Semisimple cyclic and Abelian codes. II , 1967 .

[20]  Daniel J. Costello,et al.  Polynomial weights and code constructions , 1973, IEEE Trans. Inf. Theory.

[21]  Madhu Raka,et al.  Cyclotomic numbers and primitive idempotents in the ring GF(q)[x]/(xpn-1) , 2004, Finite Fields Their Appl..

[22]  Hai Q. Dinh,et al.  Complete Distances of All Negacyclic Codes of Length Over , 2007 .

[23]  Manju Pruthi,et al.  Minimal Cyclic Codes of Length 2pn , 1999 .

[24]  Madhu Raka,et al.  Self-dual and self-orthogonal negacyclic codes of length 2pn over a finite field , 2013, Finite Fields Their Appl..

[25]  Hai Quang Dinh,et al.  On the linear ordering of some classes of negacyclic and cyclic codes and their distance distributions , 2008, Finite Fields Their Appl..

[26]  H. Q. Dinh,et al.  Negacyclic codes of length 2/sup s/ over galois rings , 2005, IEEE Transactions on Information Theory.

[27]  Hongwei Liu,et al.  Constacyclic codes over finite fields , 2012, Finite Fields Their Appl..

[28]  M. Esmaeili,et al.  On complementary-dual quasi-cyclic codes , 2009, Finite Fields Their Appl..

[29]  Hai Q. Dinh.  Structure of repeated-root constacyclic codes of length 3ps and their duals , 2013, Discret. Math..

[30]  Shixin Zhu,et al.  On the distances of cyclic codes of length 2e over Z4 , 2010, Discret. Math..

[31]  Madhu Raka,et al.  A class of constacyclic codes over a finite field-II , 2012, Indian Journal of Pure and Applied Mathematics.

[32]  Ana Salagean,et al.  Repeated-root cyclic and negacyclic codes over a finite chain ring , 2006, Discret. Appl. Math..