Abstract
Let an $[n,k,d]_q$ code be a linear code of length $n$, dimension $k$ and minimum Hamming distance $d$ over $GF(q)$. One of the most important problems in coding theory is to construct codes with optimal minimum distances. In this paper 22 new ternary linear codes are presented. Two of them are optimal. All new codes improve the respective lower bounds in [11].
Highlights
Let an [n, k, d]q code be a linear code of length n, dimension k and minimum Hamming distance d over GF (q)
Let an [n, k, d]q code be a linear code of length n, dimension k and minimum Hamming distance d over a finite field GF (q)
One of the most important and fundamental problems in coding theory is to find the optimal values of the parameters of a linear code
Summary
Let an [n, k, d]q code be a linear code of length n, dimension k and minimum Hamming distance d over a finite field GF (q). The problem of finding the parameters of optimal codes is a very difficult one and has two aspects one involves the construction of new codes with better minimum distances and the other is proving the nonexistence of codes with given parameters. It has been solved only over small finite fields for small dimensions and co-dimensions. Grassl [11] maintains a table with lower and upper bounds on minimum distances of linear codes over small finite fields GF(q) (q ≤ 9). In Theorem 4.2 five new codes are presented
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