Gilbert-Varshamov type bounds for linear codes over finite chain rings

Previous Article
Duality between packings and coverings of the Hamming space
AMC Home
This Issue
Next Article
s-extremal additive $\mathbb F_4$ codes

February 2007, 1(1): 99-109. doi: 10.3934/amc.2007.1.99

Gilbert-Varshamov type bounds for linear codes over finite chain rings

1.	Department of Mathematics, Middle East Technical University, Ínönü Bulvarı, 06531, Ankara, Turkey
2.	CNRS, I3S, ESSI, BP 145, Route des Colles, 06 903 Sophia Antipolis

Received June 2006 Revised August 2006 Published January 2007

Abstract
Related Papers

We obtain finite and asymptotic Gilbert-Varshamov type bounds for linear codes over finite chain rings with various weights.

Keywords: Gilbert-Varshamov bound, asymptotic bounds., Linear codes over rings.

Mathematics Subject Classification: Primary: 94B65, 94B60; Secondary: 16P1.

Citation: Ferruh Özbudak, Patrick Solé. Gilbert-Varshamov type bounds for linear codes over finite chain rings. Advances in Mathematics of Communications, 2007, 1 (1) : 99-109. doi: 10.3934/amc.2007.1.99

[1]	Nabil Bennenni, Kenza Guenda, Sihem Mesnager. DNA cyclic codes over rings. Advances in Mathematics of Communications, 2017, 11 (1) : 83-98. doi: 10.3934/amc.2017004
[2]	Aicha Batoul, Kenza Guenda, T. Aaron Gulliver. Some constacyclic codes over finite chain rings. Advances in Mathematics of Communications, 2016, 10 (4) : 683-694. doi: 10.3934/amc.2016034
[3]	Somphong Jitman, San Ling, Patanee Udomkavanich. Skew constacyclic codes over finite chain rings. Advances in Mathematics of Communications, 2012, 6 (1) : 39-63. doi: 10.3934/amc.2012.6.39
[4]	Kanat Abdukhalikov. On codes over rings invariant under affine groups. Advances in Mathematics of Communications, 2013, 7 (3) : 253-265. doi: 10.3934/amc.2013.7.253
[5]	Delphine Boucher, Patrick Solé, Felix Ulmer. Skew constacyclic codes over Galois rings. Advances in Mathematics of Communications, 2008, 2 (3) : 273-292. doi: 10.3934/amc.2008.2.273
[6]	Eimear Byrne. On the weight distribution of codes over finite rings. Advances in Mathematics of Communications, 2011, 5 (2) : 395-406. doi: 10.3934/amc.2011.5.395
[7]	Steven T. Dougherty, Esengül Saltürk, Steve Szabo. Codes over local rings of order 16 and binary codes. Advances in Mathematics of Communications, 2016, 10 (2) : 379-391. doi: 10.3934/amc.2016012
[8]	Jean Creignou, Hervé Diet. Linear programming bounds for unitary codes. Advances in Mathematics of Communications, 2010, 4 (3) : 323-344. doi: 10.3934/amc.2010.4.323
[9]	Sergio R. López-Permouth, Steve Szabo. On the Hamming weight of repeated root cyclic and negacyclic codes over Galois rings. Advances in Mathematics of Communications, 2009, 3 (4) : 409-420. doi: 10.3934/amc.2009.3.409
[10]	Thomas Westerbäck. Parity check systems of nonlinear codes over finite commutative Frobenius rings. Advances in Mathematics of Communications, 2017, 11 (3) : 409-427. doi: 10.3934/amc.2017035
[11]	Steven T. Dougherty, Abidin Kaya, Esengül Saltürk. Cyclic codes over local Frobenius rings of order 16. Advances in Mathematics of Communications, 2017, 11 (1) : 99-114. doi: 10.3934/amc.2017005
[12]	Hai Q. Dinh, Hien D. T. Nguyen. On some classes of constacyclic codes over polynomial residue rings. Advances in Mathematics of Communications, 2012, 6 (2) : 175-191. doi: 10.3934/amc.2012.6.175
[13]	Zihui Liu, Dajian Liao. Higher weights and near-MDR codes over chain rings. Advances in Mathematics of Communications, 2018, 12 (4) : 761-772. doi: 10.3934/amc.2018045
[14]	Minjia Shi, Daitao Huang, Lin Sok, Patrick Solé. Double circulant self-dual and LCD codes over Galois rings. Advances in Mathematics of Communications, 2019, 13 (1) : 171-183. doi: 10.3934/amc.2019011
[15]	David Grant, Mahesh K. Varanasi. The equivalence of space-time codes and codes defined over finite fields and Galois rings. Advances in Mathematics of Communications, 2008, 2 (2) : 131-145. doi: 10.3934/amc.2008.2.131
[16]	J. De Beule, K. Metsch, L. Storme. Characterization results on weighted minihypers and on linear codes meeting the Griesmer bound. Advances in Mathematics of Communications, 2008, 2 (3) : 261-272. doi: 10.3934/amc.2008.2.261
[17]	Thomas Feulner. Canonization of linear codes over $\mathbb Z$₄. Advances in Mathematics of Communications, 2011, 5 (2) : 245-266. doi: 10.3934/amc.2011.5.245
[18]	Nuh Aydin, Yasemin Cengellenmis, Abdullah Dertli, Steven T. Dougherty, Esengül Saltürk. Skew constacyclic codes over the local Frobenius non-chain rings of order 16. Advances in Mathematics of Communications, 2020, 14 (1) : 53-67. doi: 10.3934/amc.2020005
[19]	Idan Goldenberg, David Burshtein. Error bounds for repeat-accumulate codes decoded via linear programming. Advances in Mathematics of Communications, 2011, 5 (4) : 555-570. doi: 10.3934/amc.2011.5.555
[20]	Beniamin Mounits, Tuvi Etzion, Simon Litsyn. New upper bounds on codes via association schemes and linear programming. Advances in Mathematics of Communications, 2007, 1 (2) : 173-195. doi: 10.3934/amc.2007.1.173

2018 Impact Factor: 0.879

American Institute of Mathematical Sciences