Seven new champion linear codes

Seven new champion linear codes

We exhibit seven linear codes exceeding the current best known minimum distance d for their dimension k and block length n. Each code is defined over F8, and their invariants [n, k, d] are given by [49, 13, 27], [49, 14, 26], [49, 16, 24], [49, 17, 23], [49, 19, 21], [49, 25, 16] and [49, 26, 15]. Our method includes an exhaustive search of all monomial evaluation codes generated by points in t...

New Binary Linear Codes

New linear codes from constacyclic codes

One of the main challenges of coding theory is to construct linear codes with the best possible parameters. Various algebraic and combinatorial methods along with computer searches are used to construct codes with better parameters. Given the computational complexity of determining the minimum distance of a code, exhaustive searches are not feasible for all but small parameter sets. Therefore, ...

New linear codes over 𝔽9

Let dg (n, k) be the maximum possible minimum Hamming distance of a linear [n, k] code over lFg• In this paper, twenty-four new linear codes over lFg are constructed which improve the table of dg(n, k) by Brouwer. Four of these codes meet the upper bound on dg (n, k) and so are optimal. A geometric interpretation of the small dimensional codes is also given.

New Ternary Linear Codes 1

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, eighteen codes are constructed which improve the known lower bounds on minimum distance.