Analysis of the distribution of the number of erasures correctable by a binary linear code and the link to low-weight codewords

2007 ◽  
Vol 1 (3) ◽  
pp. 539 ◽  
Author(s):  
M. Tomlinson ◽  
C. Tjhai ◽  
J. Cai ◽  
M. Ambroze
Keyword(s):  
Linear Code ◽  
Binary Linear Code ◽  
Low Weight

scholarly journals Even poset and a parity result for binary linear code

2006 ◽  
Vol 418 (2-3) ◽  
pp. 591-594 ◽  
Author(s):  
Yaokun Wu
Keyword(s):  
Linear Code ◽  
Binary Linear Code

Representations of Code Vertex Operator Superalgebras

2015 ◽  
Vol 22 (02) ◽  
pp. 233-250
Author(s):  
Wei Jiang
Keyword(s):  
Vertex Operator ◽  
Linear Code ◽  
Central Charge ◽  
Hamming Code ◽  
Binary Linear Code ◽  
Vertex Operator Superalgebra

We study the representations of code vertex operator superalgebras resulting from a binary linear code which contains codewords of odd weight. We also show that there exists only one set of seven mutually orthogonal conformal vectors with central charge 1/2 in the Hamming code vertex operator superalgebra [Formula: see text]. Furthermore, we classify all the irreducible weak [Formula: see text]-modules.

scholarly journals Detection and recognition of a binary linear code

2001 ◽  
Vol 111 (1-2) ◽  
pp. 199-218 ◽  
Author(s):  
Antoine Valembois
Keyword(s):  
Linear Code ◽  
Binary Linear Code ◽  
Detection And Recognition

scholarly journals Computing coset leaders and leader codewords of binary codes

2015 ◽  
Vol 14 (08) ◽  
pp. 1550128 ◽  
Author(s):  
M. Borges-Quintana ◽  
M. A. Borges-Trenard ◽  
I. Márquez-Corbella ◽  
E. Martínez-Moro
Keyword(s):  
Weight Distribution ◽  
Linear Code ◽  
Covering Radius ◽  
Efficient Algorithms ◽  
Binary Codes ◽  
Decoding Algorithm ◽  
Test Set ◽  
Binary Linear Code

In this paper we use the Gröbner representation of a binary linear code [Formula: see text] to give efficient algorithms for computing the whole set of coset leaders, denoted by [Formula: see text] and the set of leader codewords, denoted by [Formula: see text]. The first algorithm could be adapted to provide not only the Newton and the covering radius of [Formula: see text] but also to determine the coset leader weight distribution. Moreover, providing the set of leader codewords we have a test-set for decoding by a gradient-like decoding algorithm. Another contribution of this article is the relation established between zero neighbors and leader codewords.

scholarly journals Construction of strongly optimal binary linear code with sets representation

2021 ◽  
Author(s):  
Putranto Hadi Utomo ◽  
Sugi Guritman ◽  
Teduh Wulandari Mas’oed ◽  
Hadi Sumarno
Keyword(s):  
Linear Code ◽  
Binary Linear Code
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