Nonexistence Proofs for Five Ternary Linear Codes

Binary Linear Codes: New Results on Nonexistence

Ternary Linear Codes and Quadrics

For an [n, k, d]3 code C with gcd(d, 3) = 1, we define a map wG from Σ = PG(k − 1, 3) to the set of weights of codewords of C through a generator matrix G. A t-flat Π in Σ is called an (i, j)t flat if (i, j) = (|Π ∩ F0|, |Π ∩ F1|), where F0 = {P ∈ Σ | wG(P ) ≡ 0 (mod 3)}, F1 = {P ∈ Σ | wG(P ) 6≡ 0, d (mod 3)}. We give geometric characterizations of (i, j)t flats, which involve quadrics. As an a...

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.

Some New Ternary Linear Codes

Abstract: Let  q d k n , , 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 best possible minimum distances. In this paper new one-generator quasi-cyclic (QC) codes over GF (3) are presented. Some of the results are received by construction X.

Some new quasi - twisted ternary linear codes ∗

Let [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 basic and most important problems in coding theory is to construct codes with best possible minimum distances. In this paper seven quasi-twisted ternary linear codes are constructed. These codes are new and improve the best known lower bounds on the minimum distance in [6]. 2010 ...