MacWilliams Identity for M-Spotty Weight Enumerator

2010 ◽  
Vol E93-A (2) ◽  
pp. 526-531 ◽  
Author(s):  
Kazuyoshi SUZUKI ◽  
Eiji FUJIWARA
Keyword(s):  
Weight Enumerator ◽  
Macwilliams Identity

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.

scholarly journals Nonexistence of Certain Singly Even Self-Dual Codes with Minimal Shadow

10.37236/7155 ◽  
2018 ◽  
Vol 25 (1) ◽  
Author(s):  
Stefka Bouyuklieva ◽  
Masaaki Harada ◽  
Akihiro Munemasa
Keyword(s):  
Minimum Weight ◽  
Dual Code ◽  
Weight Enumerator ◽  
Dual Codes

It is known that there is no extremal singly even self-dual $[n,n/2,d]$ code with minimal shadow for $(n,d)=(24m+2,4m+4)$, $(24m+4,4m+4)$, $(24m+6,4m+4)$, $(24m+10,4m+4)$ and $(24m+22,4m+6)$. In this paper, we study singly even self-dual codes with minimal shadow having minimum weight $d-2$ for these $(n,d)$. For $n=24m+2$, $24m+4$ and $24m+10$, we show that the weight enumerator of a singly even self-dual $[n,n/2,4m+2]$ code with minimal shadow is uniquely determined and we also show that there is no singly even self-dual $[n,n/2,4m+2]$ code with minimal shadow for $m \ge 155$, $m \ge 156$ and $m \ge 160$, respectively. We demonstrate that the weight enumerator of a singly even self-dual code with minimal shadow is not uniquely determined for parameters $[24m+6,12m+3,4m+2]$ and $[24m+22,12m+11,4m+4]$.

scholarly journals The joint weight enumerator of an LCD code and its dual

2019 ◽  
Vol 257 ◽  
pp. 12-18 ◽  
Author(s):  
Adel Alahmadi ◽  
Michel Deza ◽  
Mathieu Dutour-Sikirić ◽  
Patrick Solé
Keyword(s):  
Weight Enumerator ◽  
Lcd Code
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