Nonexistence Proofs for Five Ternary Linear Codes

An [n,k, dh-code is a ternary linear code with length n, dimension k and minimum distance d. We prove that codes with parameters [110,6, 72h, [109,6,71h, [237,6,157b, [69,7,43h, and [120,9,75h do not exist

The Nonexistence of [132, 6, 86]3 Codes and [135, 6, 88]3 Codes

We prove the nonexistence of [g3(6, d), 6, d]3 codes for d = 86, 87, 88, where g3(k, d) = ∑⌈d/3i⌉ and i=0 ... k−1. This determines n3(6, d) for d = 86, 87, 88, where nq(k, d) is the minimum length n for which an [n, k, d]q code exists

New bounds for the minimum length of quaternary linear codes of dimension five

AbstractLet n4(k, d) be the smallest integer n, such that a quaternary linear [n, k, d]-code exists. The bounds n4(5, 21) ⩽ 32, n4(5, 30) = 43, n4(5, 32) = 46, n4(5, 36) = 51, n4(5,40) ⩽ 57, n4(5, 48) ⩽ 67, n4(5, 64) = 88, n4(5, 68) ⩽ 94, n4(5, 70) ⩽ 97, n4(5, 92) ⩽ 126, n4(5, 98) ⩽ 135, n4(5, 122) = 165, n4(5, 132) ⩽ 179, n4(5, 136) ⩽ 184, n4(5, 140) = 189, n4(5, 156) ⩽ 211, n4(5,162) = 219, n4(5, 164) ⩽ 222, n4(5, 166) ⩽ 225, n4(5, 173) ⩽ 234, n4(5, 194) = 261, n4(5, 204) = 273, n4(5, 208) = 279, n4(5, 212) = 284, n4(5, 214) = 287, n4(5, 216) = 290 and n4(5, 220) = 295 are proved. A [q4 + q2 + 1, 5, q4 − q3 + q2 − q]-code over GF(q) exists for every q

Nonexistence Proofs for Five Ternary Linear Codes

An [n,k, dh-code is a ternary linear code with length n, dimension k and minimum distance d. We prove that codes with parameters [110,6, 72h, [109,6,71h, [237,6,157b, [69,7,43h, and [120,9,75h do not exist

Some new ternary linear codes

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]