Information on Result #1682460
Linear OOA(2159, 755, F2, 7, 28) (dual of [(755, 7), 5126, 29]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2159, 755, F2, 2, 28) (dual of [(755, 2), 1351, 29]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2159, 1032, F2, 2, 28) (dual of [(1032, 2), 1905, 29]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2159, 2064, F2, 28) (dual of [2064, 1905, 29]-code), using
- 1 times truncation [i] based on linear OA(2160, 2065, F2, 29) (dual of [2065, 1905, 30]-code), using
- construction X applied to C([0,14]) ⊂ C([0,12]) [i] based on
- linear OA(2155, 2049, F2, 29) (dual of [2049, 1894, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 2049 | 222−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- linear OA(2133, 2049, F2, 25) (dual of [2049, 1916, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 2049 | 222−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(25, 16, F2, 3) (dual of [16, 11, 4]-code or 16-cap in PG(4,2)), using
- construction X applied to C([0,14]) ⊂ C([0,12]) [i] based on
- 1 times truncation [i] based on linear OA(2160, 2065, F2, 29) (dual of [2065, 1905, 30]-code), using
- OOA 2-folding [i] based on linear OA(2159, 2064, F2, 28) (dual of [2064, 1905, 29]-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(2159, 377, F2, 35, 28) (dual of [(377, 35), 13036, 29]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |