scholarly journals On the Weight Hierarchy of Codes Coming From Semigroups With Two Generators

2014 ◽  
Vol 60 (1) ◽  
pp. 282-295 ◽  
Author(s):  
Manuel Delgado ◽  
Jose I. Farran ◽  
Pedro A. Garcia-Sanchez ◽  
David Llena
Keyword(s):  
Weight Hierarchy

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 $2\leq n\leq 8$.

scholarly journals The weight hierarchy of the Kasami codes

1995 ◽  
Vol 145 (1-3) ◽  
pp. 133-143 ◽  
Author(s):  
Tor Helleseth ◽  
P Vijay Kumar
Keyword(s):  
Weight Hierarchy ◽  
Kasami Codes

scholarly journals On the weight hierarchy of the semiprimitive codes

1996 ◽  
Vol 152 (1-3) ◽  
pp. 185-190 ◽  
Author(s):  
Tor Helleseth ◽  
P. Vijay Kumar
Keyword(s):  
Weight Hierarchy

scholarly journals The weight hierarchy of product codes

2000 ◽  
Vol 46 (7) ◽  
pp. 2648-2651 ◽  
Author(s):  
H.G. Schaathun
Keyword(s):  
Product Codes ◽  
Weight Hierarchy

On the weight hierarchy of geometric Goppa codes

1994 ◽  
Vol 40 (3) ◽  
pp. 913-920 ◽  
Author(s):  
Kyeongcheol Yang ◽  
P.V. Kumar ◽  
H. Stichtenoth
Keyword(s):  
Goppa Codes ◽  
Geometric Goppa Codes ◽  
Weight Hierarchy

The weight hierarchy of higher dimensional Hermitian codes

1994 ◽  
Vol 40 (1) ◽  
pp. 275-278 ◽  
Author(s):  
J.W.P. Hirschfeld ◽  
M.A. Tsfasman ◽  
S.G. Vladut
Keyword(s):  
Hermitian Codes ◽  
Higher Dimensional ◽  
Weight Hierarchy

On the weight hierarchy of Goethals codes over Z/sub 4/

1998 ◽  
Vol 44 (1) ◽  
pp. 304-307 ◽  
Author(s):  
Kyeongcheol Yang ◽  
T. Helleseth
Keyword(s):  
Goethals Codes ◽  
Weight Hierarchy
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