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
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