Name
Abstract | ||
|---|---|---|
A code $${\mathcal {C}}$$ is called formally self-dual if $${\mathcal {C}}$$ and $${\mathcal {C}^{\perp}}$$ have the same weight enumerators. There are four types of nontrivial divisible formally self-dual codes over $${\mathbb {F}_2,\,\mathbb {F}_3}$$ , and $${\mathbb F_4}$$ . These codes are called extremal if their minimum distances achieve the Mallows-Sloane bound. S. Zhang gave possible lengths for which extremal self-dual codes do not exist. In this paper, we define near-extremal formally self-dual (f.s.d.) codes. With Zhang's systematic approach, we determine possible lengths for which the four types of near-extremal formally self-dual codes as well as the two types of near-extremal formally self-dual additive codes cannot exist. In particular, our result on the nonexistence of near-extremal binary f.s.d. even codes of any even length n completes all the cases since only the case 8|n was dealt with by Han and Lee. |
Year | DOI | Venue |
|---|---|---|
2009 | 10.1007/s10623-008-9244-0 | Des. Codes Cryptography |
Keywords | Field | DocType |
Extremal codes,Formally self-dual codes,Near-extremal codes,Self-dual codes,94B60 | Discrete mathematics,Combinatorics,Mathematics,Binary number | Journal |
Volume | Issue | ISSN |
51 | 1 | 0925-1022 |
Citations | PageRank | References |
4 | 0.50 | 9 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Sunghyu Han | 1 | 35 | 6.52 |
| Jon-Lark Kim | 2 | 312 | 34.62 |