ISSN:
1573-7586
Keywords:
ternary linear codes
;
finite projective geometries
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
,
Mathematics
Notes:
Abstract It has been shown by Bogdanova and Boukliev [1] that there exist a ternary [38,5,24] code and a ternary [37,5,23] code. But it is unknown whether or not there exist a ternary [39,6,24] code and a ternary [38,6,23] code. The purpose of this paper is to prove that (1) there is no ternary [39,6,24] code and (2) there is no ternary [38,6,23] code using the nonexistence of ternary [39,6,24] codes. Since it is known (cf. Brouwer and Sloane [2] and Hamada and Watamori [14]) that (i) n3(6,23) = 38〉 or 39 and d3(38,6) = 22 or 23 and (ii) n3(6,24) = 39 or 40 and d3(39,6) = 23 or 24, this implies that n3(6,23) = 39, d3(38,6) = 22, n3(6,24) = 40 and d3(39,6) = 23, where n3〈〉(k,d) and d〈〉3(n,k) denote the smallest value of n and the largest value of d, respectively, for which there exists an [n,k,d] code over the Galois field GF(3).
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1008278312966
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