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AN EFFICIENT CONSTRUCTION OF SELF-DUAL CODES
- AN EFFICIENT CONSTRUCTION OF SELF-DUAL CODES
- Kim, Jon-Lark; Lee, Yoonjin
- Ewha Authors
- SCOPUS Author ID
- Issue Date
- Journal Title
- BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY
- vol. 52, no. 3, pp. 915 - 923
- building-up construction; linear codes; self-dual codes
- KOREAN MATHEMATICAL SOC
- SCIE; SCOPUS; KCI
- Self-dual codes have been actively studied because of their connections with other mathematical areas including t-designs, invariant theory, group theory, lattices, and modular forms. We presented the building-up construction for self-dual codes over GF(q) with q as 1 (mod 4), and over other certain rings (see , ). Since then, the existence of the building-up construction for the open case over GF(q) with q = p(r) as 3 (mod 4) with an odd prime p satisfying p as 3 (mod 4) with r odd has not been solved. In this paper, we answer it positively by presenting the building-up construction explicitly. As examples, we present new optimal self-dual [16, 8, 7] codes over GF(7) and new self-dual codes over GF(7) with the best known parameters [24, 12, 9].
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