Information on Result #1438523
Linear OOA(5110, 1953181, F5, 2, 14) (dual of [(1953181, 2), 3906252, 15]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(5110, 1953181, F5, 14) (dual of [1953181, 1953071, 15]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(5109, 1953179, F5, 14) (dual of [1953179, 1953070, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(7) [i] based on
- linear OA(5100, 1953125, F5, 14) (dual of [1953125, 1953025, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(555, 1953125, F5, 8) (dual of [1953125, 1953070, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(59, 54, F5, 5) (dual of [54, 45, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(59, 62, F5, 5) (dual of [62, 53, 6]-code), using
- a “GraCyc†code from Grassl’s database [i]
- discarding factors / shortening the dual code based on linear OA(59, 62, F5, 5) (dual of [62, 53, 6]-code), using
- construction X applied to Ce(13) ⊂ Ce(7) [i] based on
- linear OA(5109, 1953180, F5, 13) (dual of [1953180, 1953071, 14]-code), using Gilbert–Varšamov bound and bm = 5109 > Vbs−1(k−1) = 107 962635 679869 702038 747868 727707 922764 792114 325209 283453 554075 376518 736285 [i]
- linear OA(50, 1, F5, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(5109, 1953179, F5, 14) (dual of [1953179, 1953070, 15]-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(5110, 976590, F5, 3, 14) (dual of [(976590, 3), 2929660, 15]-NRT-code) | [i] | OOA Folding | |