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.

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 from vectorial Boolean functions in the context of algebraic attacks

2020 ◽  
pp. 2150032
Author(s):  
M. Boumezbeur ◽  
S. Mesnager ◽  
K. Guenda
Keyword(s):  
Boolean Functions ◽  
Linear Codes ◽  
Cyclic Codes ◽  
Weight Enumerator ◽  
Direct Link ◽  
Algebraic Attacks ◽  
Vectorial Boolean Functions ◽  
Lcd Codes ◽  
Vectorial Function ◽  
The Relationship

In this paper, we study the relationship between vectorial (Boolean) functions and cyclic codes in the context of algebraic attacks. We first derive a direct link between the annihilators of a vectorial function (in univariate form) and certain [Formula: see text]-ary cyclic codes (which we show that they are LCD codes). We also present some properties of those cyclic codes as well as their weight enumerator. In addition, we generalize the so-called algebraic complement and study its properties.

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.

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