Information on Result #1515905
Linear OOA(2209, 970, F2, 3, 36) (dual of [(970, 3), 2701, 37]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2209, 970, F2, 2, 36) (dual of [(970, 2), 1731, 37]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2209, 1042, F2, 2, 36) (dual of [(1042, 2), 1875, 37]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2209, 2084, F2, 36) (dual of [2084, 1875, 37]-code), using
- 1 times truncation [i] based on linear OA(2210, 2085, F2, 37) (dual of [2085, 1875, 38]-code), using
- construction XX applied to Ce(36) ⊂ Ce(32) ⊂ Ce(30) [i] based on
- linear OA(2199, 2048, F2, 37) (dual of [2048, 1849, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(2177, 2048, F2, 33) (dual of [2048, 1871, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(2166, 2048, F2, 31) (dual of [2048, 1882, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- linear OA(21, 5, F2, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction XX applied to Ce(36) ⊂ Ce(32) ⊂ Ce(30) [i] based on
- 1 times truncation [i] based on linear OA(2210, 2085, F2, 37) (dual of [2085, 1875, 38]-code), using
- OOA 2-folding [i] based on linear OA(2209, 2084, F2, 36) (dual of [2084, 1875, 37]-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(2209, 485, F2, 5, 36) (dual of [(485, 5), 2216, 37]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(2209, 485, F2, 6, 36) (dual of [(485, 6), 2701, 37]-NRT-code) | [i] | ||