Information on Result #1689131
Linear OOA(2251, 2032, F2, 7, 39) (dual of [(2032, 7), 13973, 40]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2251, 2032, F2, 4, 39) (dual of [(2032, 4), 7877, 40]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2251, 2052, F2, 4, 39) (dual of [(2052, 4), 7957, 40]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2251, 8208, F2, 39) (dual of [8208, 7957, 40]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2249, 8206, F2, 39) (dual of [8206, 7957, 40]-code), using
- construction X applied to Ce(38) ⊂ Ce(36) [i] based on
- linear OA(2248, 8192, F2, 39) (dual of [8192, 7944, 40]-code), using an extension Ce(38) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(2235, 8192, F2, 37) (dual of [8192, 7957, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(21, 14, F2, 1) (dual of [14, 13, 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 X applied to Ce(38) ⊂ Ce(36) [i] based on
- 2 times code embedding in larger space [i] based on linear OA(2249, 8206, F2, 39) (dual of [8206, 7957, 40]-code), using
- OOA 4-folding [i] based on linear OA(2251, 8208, F2, 39) (dual of [8208, 7957, 40]-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(2251, 677, F2, 49, 39) (dual of [(677, 49), 32922, 40]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row |