Name
Abstract | ||
|---|---|---|
Skew Hadamard designs (4n --- 1, 2n --- 1, n --- 1) are associated to order 4n skew Hadamard matrices in the natural way. We study the codes spanned by their incidence matrices A and by I + A and show that they are self-dual after extension (resp. extension and augmentation) over fields of characteristic dividing n. Quadratic Residues codes are obtained in the case of the Paley matrix. Results on the p-rank of skew Hadamard designs are rederived in that way. Codes from skew Hadamard designs are classified. An optimal self-dual code over GF(5) is rediscovered in length 20. Six new inequivalent [56, 28, 16] self-dual codes over GF(7) are obtained from skew Hadamard matrices of order 56, improving the only known quadratic double circulant code of length 56 over GF(7). |
Year | DOI | Venue |
|---|---|---|
2008 | 10.1007/s10623-008-9173-y | Des. Codes Cryptography |
Keywords | Field | DocType |
Skew Hadamard designs,Self-dual codes,05B20,94B25 | Discrete mathematics,Hadamard's maximal determinant problem,Combinatorics,Hadamard matrix,Paley construction,Linear code,Hadamard's inequality,Complex Hadamard matrix,Hadamard transform,Hadamard code,Mathematics | Journal |
Volume | Issue | ISSN |
49 | 1-3 | 0925-1022 |
Citations | PageRank | References |
3 | 0.47 | 9 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jon-Lark Kim | 1 | 312 | 34.62 |
| Patrick Solé | 2 | 636 | 89.68 |