The MacWilliams Identity for Linear Codes over Galois Rings

2000 ◽  
pp. 333-338 ◽  
Author(s):  
Zhe-Xian Wan
Keyword(s):  
Linear Codes ◽  
Galois Rings ◽  
Macwilliams Identity

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.

Linear codes over 𝔽4R and their MacWilliams identity

2020 ◽  
Vol 12 (06) ◽  
pp. 2050085
Author(s):  
Nasreddine Benbelkacem ◽  
Martianus Frederic Ezerman ◽  
Taher Abualrub
Keyword(s):  
Commutative Ring ◽  
Linear Codes ◽  
Inner Product ◽  
Dual Codes ◽  
Macwilliams Identity ◽  
Generator Matrices

Let [Formula: see text] be the field of four elements. We denote by [Formula: see text] the commutative ring, with [Formula: see text] elements, [Formula: see text] with [Formula: see text]. This work defines linear codes over the ring of mixed alphabets [Formula: see text] as well as their dual codes under a nondegenerate inner product. We then derive the systematic form of the respective generator matrices of the codes and their dual codes. We wrap the paper up by proving the MacWilliams identity for linear codes over [Formula: see text].

Decoding of linear codes over Galois rings

2001 ◽  
Vol 47 (4) ◽  
pp. 1599-1603 ◽  
Author(s):  
N.S. Babu ◽  
K.-H. Zimmermann
Keyword(s):  
Linear Codes ◽  
Galois Rings

The MacWilliams Identity of Linear Codes over Mn×s(Fp+uFp+vFp+uvFp) with Respect to RT Metric

2014 ◽  
Vol 571-572 ◽  
pp. 262-266 ◽  
Author(s):  
Yan Liu ◽  
Min Jia Shi
Keyword(s):  
Linear Codes ◽  
Weight Enumerator ◽  
Macwilliams Identity ◽  
Definition Of

The definition of the exact complete ρ weight enumerator over Mn×s(Fp+uFp+vFp+uvFp) is given, and the MacWilliams identity with respect to RT metric for the exact complete ρ weight enumerator of linear codes over Mn×s(Fp+uFp+vFp+uvFp) is obtained. Finally, a example is presented to illustrate the obtained results.

Sign in / Sign up

Export Citation Format

Share Document