New bounds for n4( k, d) and classification of some optimal codes over GF(4)

• Published in: Discrete mathematics Vol. 281; no. 1; pp. 43 - 66
• Main Authors: Bouyukliev, Iliya, Grassl, Markus, Varbanov, Zlatko
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01-04-2004; Elsevier
• Subjects: Algebraic combinatorics; Bounds on codes; Combinatorics; Combinatorics. Ordered structures; Exact sciences and technology; Mathematics; Optimal codes; Quaternary linear codes; Sciences and techniques of general use; Optimal codes; Bounds on codes; Quaternary linear codes; Discrete mathematics; Linear code; Combinatorics; Classification
• ISSN: 0012-365X; 1872-681X
• DOI: 10.1016/j.disc.2003.11.003

Let
n
4(
k,
d) be the minimum length of a linear [
n,
k,
d] code over GF(4) for given values of
k and
d. For codes of dimension five, we compute the exact values of
n
4(5,
d) for 75 previously open cases. Additionally, we show that
n
4(6,14)=24,
n
4(7,9)=18, and
n
4(7,10)=20. Moreover, we classify optimal quaternary codes for some values of
n and
k.