Extendability of linear codes over GF(q) with minimum distance d, gcd(d,q)=1

Extendability of linear codes over Fq

For an [n, k, d]q code C, we define a mapping wC from PG(k − 1, q) to the set of weights of C via a generator matrix of C. We give a geometric aspect derived from wC to investigate the extendability of linear codes. We survey known extension theorems and some recent results.

New minimum distance bounds for linear codes over GF(5)

Let [n; k; d]q-codes be linear codes of length n, dimension k and minimum Hamming distance d over GF(q). In this paper, 32 new codes over GF(5) are constructed and the nonexistence of 51 codes is proved. c © 2003 Elsevier B.V. All rights reserved.

Construction of linear codes with prescribed minimum distance

We construct linear codes over finite fields with prescribed minimum distance by selectiong columns of the generator matrix. This selection problem can be formulated as an integer programming problem. In order to reduce the search space we prescribe a group of automorphisms. Then, in many cases the resulting integer programming problem can be solved by lattice point enumeration. With this appro...

Linear Binary Error Correcting Codes with Specified Minimum Hamming Distance

Computation of Minimum Hamming Weight for Linear Codes

In this paper, we consider the minimum Hamming weight for linear codes over special finite quasi-Frobenius rings. Furthermore, we obtain minimal free $R$-submodules of a finite quasi-Frobenius ring $R$  which contain a linear code and derive the relation between their minimum Hamming weights. Finally, we suggest an algorithm that computes this weight using the Grobner basis and we show that und...