126 research outputs found
Binary and Ternary Quasi-perfect Codes with Small Dimensions
The aim of this work is a systematic investigation of the possible parameters
of quasi-perfect (QP) binary and ternary linear codes of small dimensions and
preparing a complete classification of all such codes. First we give a list of
infinite families of QP codes which includes all binary, ternary and quaternary
codes known to is. We continue further with a list of sporadic examples of
binary and ternary QP codes. Later we present the results of our investigation
where binary QP codes of dimensions up to 14 and ternary QP codes of dimensions
up to 13 are classified.Comment: 4 page
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) β©½ 32, n4(5, 30) = 43, n4(5, 32) = 46, n4(5, 36) = 51, n4(5,40) β©½ 57, n4(5, 48) β©½ 67, n4(5, 64) = 88, n4(5, 68) β©½ 94, n4(5, 70) β©½ 97, n4(5, 92) β©½ 126, n4(5, 98) β©½ 135, n4(5, 122) = 165, n4(5, 132) β©½ 179, n4(5, 136) β©½ 184, n4(5, 140) = 189, n4(5, 156) β©½ 211, n4(5,162) = 219, n4(5, 164) β©½ 222, n4(5, 166) β©½ 225, n4(5, 173) β©½ 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 β q3 + q2 β q]-code over GF(q) exists for every q
Optimal additive quaternary codes of low dimension
An additive quaternary -code (length quaternary dimension
minimum distance ) is a -dimensional F_2-vector space of -tuples with
entries in (the -dimensional vector space over F_2) with
minimum Hamming distance We determine the optimal parameters of additive
quaternary codes of dimension The most challenging case is dimension
We prove that an additive quaternary -code where
exists if and only if . In particular we construct new optimal -dimensional additive
quaternary codes. As a by-product we give a direct proof for the fact that a
binary linear -code for exists if and only if the Griesmer
bound is
satisfied.Comment: 7 page
Cocyclic simplex codes of type alpha over Z4 and Z2s
Over the past decade, cocycles have been used to construct Hadamard and generalized Hadamard matrices. This, in turn, has led to the construction of codes-self-dual and others. Here we explore these ideas further to construct cocyclic complex and Butson-Hadamard matrices, and subsequently we use the matrices to construct simplex codes of type /spl alpha/ over Z(4) and Z(2/sup s/), respectively
- β¦