COMPARISON OF THE LEE AND HOMOGENOUS WEIGHTS OVER A FAMILY OF CHAIN RINGS |
Alahmadi, Adel
(Department of Mathematics King Abdulaziz University)
Alkenani, Ahmad (Department of Mathematics King Abdulaziz University) Alomari, Rahmah (Department of Mathematics King Abdulaziz University) Muthana, Najat (Department of Mathematics King Abdulaziz University) Sole, Patrick (Department of Mathematics University of Paris 8) Yildiz, Bahattin (Department of Mathematics Northern Arizona University) |
1 | G. Andrews, A. Klein, and M. J. Strauss, Groups, Algebras, and Applications, Pages 4-5, Library of Congress Cataloging-in-Publication Data, 18, 2009. |
2 | W. Bosma and J. Cannon, Handbook of Magma Functions, Sydney, 1995. |
3 | I. Constantinescu and W. Heise, A metric for codes over residue class rings of integers, Transmission 33 (1997), no. 3, 208-213 (1998); translated from Problemy Peredachi Informatsii 33 (1997), no. 3, 22-28. |
4 | S. T. Dougherty, S. Karadeniz, and B. Yildiz, Cyclic codes over , Des. Codes Cryptogr. 63 (2012), no. 1, 113-126. DOI |
5 | S. T. Dougherty, J.-L. Kim, H. Kulosman, and H. Liu, Self-dual codes over commutative Frobenius rings, Finite Fields Appl. 16 (2010), no. 1, 14-26. DOI |
6 | S. T. Dougherty, B. Yildiz, and S. Karadeniz, Codes over , Gray maps and their binary images, Finite Fields Appl. 17 (2011), no. 3, 205-219. DOI |
7 | M. Grassl, Bounds on the minimum distance of linear codes and quantum codes, Online available at www.codetables.de. |
8 | M. Greferath, G. McGuire, and M. E. O'Sullivan, On Plotkin-optimal codes over finite Frobenius rings, J. Algebra Appl. 5 (2006), no. 6, 799-815. DOI |
9 | M. Greferath and S. E. Schmidt, Finite-ring combinatorics and MacWilliams' equivalence theorem, J. Combin. Theory Ser. A 92 (2000), no. 1, 17-28. DOI |
10 | T. Honold, Characterization of finite Frobenius rings, Arch. Math. (Basel) 76 (2001), no. 6, 406-415. DOI |
11 | Z. O. Ozger, U. U. Kara, and B. Yildiz, Linear, cyclic and constacyclic codes over , Filomat 28 (2014), no. 5, 897-906. DOI |
12 | B. Yildiz and S. Karadeniz, Cyclic codes over , Des. Codes Cryptogr. 58 (2011), no. 3, 221-234. DOI |
13 | I. Siap, T. Abualrub, and B. Yildiz, One generator quasi-cyclic codes over , J. Franklin Inst. 349 (2012), no. 1, 284-292. DOI |
14 | N. Tufekci and B. Yildiz, On codes over and constructions for new binary self-dual codes, Math. Slovaca 66 (2016), no. 6, 1511-1526. |
15 | J. A. Wood, Duality for modules over finite rings and applications to coding theory, Amer. J. Math. 121 (1999), no. 3, 555-575. DOI |
16 | B. Yildiz and I. G. Kelebek, The homogeneous weight for , related Gray map and new binary quasi-cyclic codes, Filomat 31 (2017), no. 4, 885-897. DOI |