scholarly journals On the weight hierarchy of locally repairable codes

Author(s):  
Jie Hao ◽  
Shu-Tao Xia ◽  
Bin Chen ◽  
Fang-Wei Fu
2021 ◽  
Vol 67 (1) ◽  
pp. 217-231
Author(s):  
Bin Chen ◽  
Weijun Fang ◽  
Shu-Tao Xia ◽  
Jie Hao ◽  
Fang-Wei Fu

2018 ◽  
Vol 64 (4) ◽  
pp. 2499-2511 ◽  
Author(s):  
Bin Chen ◽  
Shu-Tao Xia ◽  
Jie Hao ◽  
Fang-Wei Fu

Author(s):  
Farzaneh Farhang Baftani ◽  
Hamid Reza Maimani

The support of an $(n, M, d)$ binary code  $C$ over the set $\mathbf{A}=\{0,1\}$ is the set of all coordinate positions $i$, such  that  at  least two codewords  have distinct entry  in  coordinate $i$.  The  $r$th  generalized  Hamming  weight  $d_r(C)$,  $1\leq r\leq 1+log_2n+1$,  of  $C$  is  defined  as  the minimum  of  the  cardinalities  of  the  supports  of  all subset  of  $C$ of cardinality $2^{r-1}+1$.  The  sequence $(d_1(C), d_2(C), \ldots, d_k(C))$ is called the Hamming weight hierarchy (HWH) of $C$. In this paper we obtain HWH for $(2^k-1, 2^k, 2^{k-1}$ binary Hadamard code corresponding to Sylvester Hadamard matrix $H_{2^k}$ and we show that    $$d_r=2^{k-r} (2^r -1).$$ Also we compute the HWH of all $(4n-1, 4n, 2n)$ Hadamard code for $2\leq n\leq 8$.


2019 ◽  
Vol 65 (1) ◽  
pp. 108-117 ◽  
Author(s):  
Xudong Li ◽  
Liming Ma ◽  
Chaoping Xing

Sign in / Sign up

Export Citation Format

Share Document