Beelen, Peter Singh, Prasant

In this article we consider linear codes coming from skew-symmetric determinantal varieties, which are defined by the vanishing of minors of a certain fixed size in the space of skew-symmetric matrices. In odd characteristic, the minimum distances of these codes are determined and a recursive formula for the weight of a general codeword in these co...

Beelen, Peter Singh, Prasant

In this article we consider linear codes coming from skew-symmetric determinantal varieties, which are defined by the vanishing of minors of a certain fixed size in the space of skew-symmetric matrices. In odd characteristic, the minimum distances of these codes are determined and a recursive formula for the weight of a general codeword in these co...

Beelen, Peter Singh, Prasant

In this article we consider linear codes coming from skew-symmetric determinantal varieties, which are defined by the vanishing of minors of a certain fixed size in the space of skew-symmetric matrices. In odd characteristic, the minimum distances of these codes are determined and a recursive formula for the weight of a general codeword in these co...

Beelen, Peter Singh, Prasant

In this article we consider linear codes coming from skew-symmetric determinantal varieties, which are defined by the vanishing of minors of a certain fixed size in the space of skew-symmetric matrices. In odd characteristic, the minimum distances of these codes are determined and a recursive formula for the weight of a general codeword in these co...

Beelen, Peter Singh, Prasant

In this article we consider linear codes coming from skew-symmetric determinantal varieties, which are defined by the vanishing of minors of a certain fixed size in the space of skew-symmetric matrices. In odd characteristic, the minimum distances of these codes are determined and a recursive formula for the weight of a general codeword in these co...

Charpin, Pascale Peng, Jie

The associated codes of almost perfect nonlinear (APN) functions have been widely studied. In this paper we consider more generally the codes associated with functions that have differential uniformity at least 4. We emphasize, for such a function F , the role of codewords of weight 3 and 4 and of some cosets of its associated code C F. We give som...

Ebrahimi, Mohammad Izadara, Alireza
Published in
Soft Computing

This paper defines the concept of ideal entropy for BCI-algebras in general, and it tries to describe some of its properties. Moreover, the present study will show that F2n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} ...

Li, Ping Guo, Xuemei Zhu, Shixin Kai, Xiaoshan
Published in
Journal of Applied Mathematics and Computing

In this paper, we mainly study the theory of linear codes over the ring R=Z4+uZ4+vZ4+uvZ4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R =\mathbb {Z}_4+u\mathbb {Z}_4...

Dück, Natalia Márquez-Corbella, Irene Martínez-Moro, Edgar

We will show how one can compute all reduced Gröbner bases with re-spect to a degree compatible ordering for code ideals -even though these binomial ideals are not toric. To this end, the correspondence of linear codes and binomial ideals will be briefly described as well as their resemblance to toric ideals. Finally, we will hint at applications o...

Greferath, Marcus Honold, Thomas Mc Fadden, Cathy Wood, Jay A. Zumbrägel, Jens
Published in
Journal of Combinatorial Theory, Series A

A finite ring R and a weight w on R satisfy the Extension Property if every R-linear w-isometry between two R-linear codes in Rn extends to a monomial transformation of Rn that preserves w. MacWilliams proved that finite fields with the Hamming weight satisfy the Extension Property. It is known that finite Frobenius rings with either the Hamming we...