Macwilliams identities of linear codes over the ring F 2 + uF 2 + vF 2

2015 ◽  
Vol 28 (3) ◽  
pp. 691-701
Author(s):  
Xiusheng Liu ◽  
Hualu Liu
Keyword(s):  
Linear Codes ◽  
Macwilliams Identities

THE EQUIVALENT IDENTITIES OF THE MACWILLIAMS IDENTITIES FOR LINEAR CODES

2015 ◽  
Vol 76 (1) ◽  
Author(s):  
Bao Xiaomin
Keyword(s):  
Linear Codes ◽  
Macwilliams Identity ◽  
Macwilliams Identities

We use derivatives to prove the equivalences between MacWilliams identity and its four equivalent forms, and present new interpretations for the four equivalent forms.

scholarly journals Constacyclic codes over 𝔽pm[u1, u2,⋯,uk]/〈 ui2 = ui, uiuj = ujui〉

2018 ◽  
Vol 16 (1) ◽  
pp. 490-497
Author(s):  
Xiying Zheng ◽  
Bo Kong
Keyword(s):  
Linear Codes ◽  
Gray Map ◽  
Constacyclic Codes ◽  
Macwilliams Identities

AbstractIn this paper, we study linear codes over ring Rk = 𝔽pm[u1, u2,⋯,uk]/〈$\begin{array}{} u^{2}_{i} \end{array} $ = ui, uiuj = ujui〉 where k ≥ 1 and 1 ≤ i, j ≤ k. We define a Gray map from $\begin{array}{} R_{k}^n\,\,\text{to}\,\,{\mathbb F}_{p^m}^{2^kn} \end{array} $ and give the generator polynomials of constacyclic codes over Rk. We also study the MacWilliams identities of linear codes over Rk.

scholarly journals On the MacWilliams identities for linear codes

1988 ◽  
Vol 107 ◽  
pp. 181-189 ◽  
Author(s):  
Richard A. Brualdi ◽  
Vera S. Pless ◽  
Janet S. Beissinger
Keyword(s):  
Linear Codes ◽  
Macwilliams Identities

MACWILLIAMS IDENTITIES FOR WEIGHT ENUMERATORS WITH RESPECT TO THE RT METRIC

2014 ◽  
Vol 06 (02) ◽  
pp. 1450030 ◽  
Author(s):  
AMIT K. SHARMA ◽  
ANURADHA SHARMA
Keyword(s):  
Algebraic Structure ◽  
Linear Code ◽  
Linear Codes ◽  
Error Correcting Codes ◽  
Weight Enumerator ◽  
Weight Enumerators ◽  
Ring Of Integers ◽  
The Past ◽  
Macwilliams Identities ◽  
Hamming Metric

Linear codes constitute an important family of error-correcting codes and have a rich algebraic structure. Initially, these codes were studied with respect to the Hamming metric; while for the past few years, they are also studied with respect to a non-Hamming metric, known as the Rosenbloom–Tsfasman metric (also known as RT metric or ρ metric). In this paper, we introduce and study the split ρ weight enumerator of a linear code in the R-module Mn×s(R) of all n × s matrices over R, where R is a finite Frobenius commutative ring with unity. We also define the Lee complete ρ weight enumerator of a linear code in Mn×s(ℤk), where ℤk is the ring of integers modulo k ≥ 2. We also derive the MacWilliams identities for each of these ρ weight enumerators.

scholarly journals Linear Codes Over a Non-Chain Ring and the MacWilliams Identities

IEEE Access ◽  
2020 ◽  
Vol 8 ◽  
pp. 87115-87120
Author(s):  
Tiantian Li ◽  
Rongsheng Wu ◽  
Juan Xu
Keyword(s):  
Linear Codes ◽  
Chain Ring ◽  
Macwilliams Identities
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