Asymptotic bounds on the covering radius of binary codes

1990 ◽  
Vol 36 (6) ◽  
pp. 1470-1472 ◽  
Author(s):  
P. Sole
Keyword(s):  
Covering Radius ◽  
Binary Codes ◽  
Asymptotic Bounds

Bounds for abnormal binary codes with covering radius one

1991 ◽  
Vol 37 (2) ◽  
pp. 372-375 ◽  
Author(s):  
H.S. Honkala ◽  
H.O. Hamalainen
Keyword(s):  
Covering Radius ◽  
Binary Codes

On the covering radius of binary codes (Corresp.)

1978 ◽  
Vol 24 (5) ◽  
pp. 627-628 ◽  
Author(s):  
T. Helleseth ◽  
T. Klove ◽  
J. Mykkeltveit
Keyword(s):  
Covering Radius ◽  
Binary Codes

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 Ternary Covering Codes

10.37236/1281 ◽  
1996 ◽  
Vol 3 (2) ◽  
Author(s):  
Laurent Habsieger
Keyword(s):  
Lower Bounds ◽  
Covering Radius ◽  
Linear Inequalities ◽  
Characteristic Functions ◽  
Binary Codes ◽  
Covering Codes ◽  
Congruence Properties

In [5], we studied binary codes with covering radius one via their characteristic functions. This gave us an easy way of obtaining congruence properties and of deriving interesting linear inequalities. In this paper we extend this approach to ternary covering codes. We improve on lower bounds for ternary $1$-covering codes, the so-called football pool problem, when $3$ does not divide $n-1$. We also give new lower bounds for some covering codes with a covering radius greater than one.

On the size of optimal binary codes of length 9 and covering radius 1

2001 ◽  
Vol 47 (6) ◽  
pp. 2556-2557 ◽  
Author(s):  
P.R.J. Ostergard ◽  
U. Blass
Keyword(s):  
Covering Radius ◽  
Binary Codes
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