On the second generalized Hamming weight of the dual code of a double-error-correcting binary BCH code

1995 ◽  
Vol 41 (3) ◽  
pp. 805-808 ◽  
Author(s):  
Changshik Shim ◽  
Habong Chung
Keyword(s):  
Dual Code ◽  
Bch Code ◽  
Hamming Weight ◽  
Generalized Hamming Weight

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

Extended maximal self-orthogonal codes

2019 ◽  
Vol 11 (05) ◽  
pp. 1950052
Author(s):  
Yilmaz Durğun
Keyword(s):  
Dual Code ◽  
Weight Enumerator ◽  
Hamming Weight ◽  
Golay Code ◽  
Orthogonal Codes ◽  
Orthogonal Code ◽  
Binary Golay Code

Self-dual and maximal self-orthogonal codes over [Formula: see text], where [Formula: see text] is even or [Formula: see text](mod 4), are extensively studied in this paper. We prove that every maximal self-orthogonal code can be extended to a self-dual code as in the case of binary Golay code. Using these results, we show that a self-dual code can also be constructed by gluing theory even if the sum of the lengths of the gluing components is odd. Furthermore, the (Hamming) weight enumerator [Formula: see text] of a self-dual code [Formula: see text] is given in terms of a maximal self-orthogonal code [Formula: see text], where [Formula: see text] is obtained by the extension of [Formula: see text].

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