Name
Abstract | ||
|---|---|---|
Crnković (2014) introduced a self-orthogonal 2 q , q - 1 code and a self-dual 2 q + 2 , q + 1 code over the finite field F p arising from orbit matrices for Menon designs, for every prime power q , where q ź 1 ( mod 4 ) and p a prime dividing q + 1 2 . He showed that if q is a prime and q = 12 m + 5 , where m is a non-negative integer, then the self-dual 2 q + 2 , q + 1 code over F 3 is equivalent to a Pless symmetry code. However for other values of q , he remarked that these codes, up to his knowledge, do not belong to some previously known series of codes. In this paper, we describe an equivalence between his self-dual codes and the known codes introduced by Gaboritźin 2002. On the other hand, Crnković (2014) also conjectured that if p = q + 1 2 is a prime, the self-orthogonal code and the self-dual code have minimum distance p + 3 . We disprove this conjecture by giving two counter-examples in the case of the self-orthogonal code and the self-dual code, respectively when q = 25 and p = 13 . |
Year | DOI | Venue |
|---|---|---|
2016 | 10.1016/j.disc.2016.03.016 | Discrete Mathematics |
Keywords | Field | DocType |
Block design,Linear codes,Self-dual codes,Orbit matrix | Integer,Prime (order theory),Discrete mathematics,Combinatorics,Finite field,Group code,Circulant matrix,Linear code,Prime power,Conjecture,Mathematics | Journal |
Volume | Issue | ISSN |
339 | 9 | 0012-365X |
Citations | PageRank | References |
0 | 0.34 | 3 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Dong-Man Heo | 1 | 0 | 0.34 |
| Jon-Lark Kim | 2 | 312 | 34.62 |