The Second Generalized Hamming Weight of the Dual Codes of Double-Error Correcting Binary BCH-Codes

1995 ◽  
Vol 27 (1) ◽  
pp. 82-86 ◽  
Author(s):  
G. Van Der Geer ◽  
M. Van Der Vlugt
Keyword(s):  
Bch Codes ◽  
Hamming Weight ◽  
Dual Codes ◽  
Generalized Hamming Weight

scholarly journals On the generalized Hamming weights of certain Reed–Muller-type codes

2020 ◽  
Vol 28 (1) ◽  
pp. 205-217
Author(s):  
Manuel González-Sarabia ◽  
Delio Jaramillo ◽  
Rafael H. Villarreal
Keyword(s):  
Finite Field ◽  
Hamming Weight ◽  
Combinatorial Formula ◽  
Dual Codes ◽  
Generalized Hamming Weight ◽  
Generalized Hamming Weights ◽  
Basic Parameters ◽  
Hamming Weights

AbstractThere is a nice combinatorial formula of P. Beelen and M. Datta for the r-th generalized Hamming weight of an a ne cartesian code. Using this combinatorial formula we give an easy to evaluate formula to compute the r-th generalized Hamming weight for a family of a ne cartesian codes. If 𝕏 is a set of projective points over a finite field we determine the basic parameters and the generalized Hamming weights of the Veronese type codes on 𝕏 and their dual codes in terms of the basic parameters and the generalized Hamming weights of the corresponding projective Reed–Muller-type codes on 𝕏 and their dual codes.

The second generalized Hamming weight of certain Castle codes

2014 ◽  
Vol 76 (1) ◽  
pp. 81-87 ◽  
Author(s):  
Wilson Olaya-León ◽  
Claudia Granados-Pinzón
Keyword(s):  
Hamming Weight ◽  
Generalized Hamming Weight ◽  
Castle Codes

scholarly journals THE WEIGHT HIERARCHY OF HADAMARD CODES

2019 ◽  
pp. 797
Author(s):  
Farzaneh Farhang Baftani ◽  
Hamid Reza Maimani
Keyword(s):  
Binary Code ◽  
Hadamard Matrix ◽  
Hamming Weight ◽  
Generalized Hamming Weight ◽  
Hadamard Codes ◽  
Hadamard Code ◽  
Weight Hierarchy

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 $2\leq n\leq 8$.

Network Generalized Hamming Weight

2011 ◽  
Vol 57 (2) ◽  
pp. 1136-1143 ◽  
Author(s):  
Chi-Kin Ngai ◽  
Raymond W. Yeung ◽  
Zhixue Zhang
Keyword(s):  
Hamming Weight ◽  
Generalized Hamming Weight
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