Information on Result #1428422
Linear OOA(4199, 16445, F4, 2, 35) (dual of [(16445, 2), 32691, 36]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(4199, 16445, F4, 35) (dual of [16445, 16246, 36]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(4197, 16441, F4, 35) (dual of [16441, 16244, 36]-code), using
- construction X applied to C([0,17]) ⊂ C([0,13]) [i] based on
- linear OA(4183, 16385, F4, 35) (dual of [16385, 16202, 36]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,17], and minimum distance d ≥ |{−17,−16,…,17}|+1 = 36 (BCH-bound) [i]
- linear OA(4141, 16385, F4, 27) (dual of [16385, 16244, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(414, 56, F4, 7) (dual of [56, 42, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(414, 65, F4, 7) (dual of [65, 51, 8]-code), using
- a “GraXX†code from Grassl’s database [i]
- discarding factors / shortening the dual code based on linear OA(414, 65, F4, 7) (dual of [65, 51, 8]-code), using
- construction X applied to C([0,17]) ⊂ C([0,13]) [i] based on
- linear OA(4197, 16443, F4, 34) (dual of [16443, 16246, 35]-code), using Gilbert–Varšamov bound and bm = 4197 > Vbs−1(k−1) = 8301 460968 174328 472586 192372 018618 735699 236278 091268 207983 224466 311168 108113 147307 121069 062868 630606 144670 217355 190709 [i]
- linear OA(40, 2, F4, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(4197, 16441, F4, 35) (dual of [16441, 16244, 36]-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(4199, 8222, F4, 3, 35) (dual of [(8222, 3), 24467, 36]-NRT-code) | [i] | OOA Folding | |