Information on Result #1432332
Linear OOA(4232, 65626, F4, 2, 35) (dual of [(65626, 2), 131020, 36]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(4232, 65626, F4, 35) (dual of [65626, 65394, 36]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(4230, 65622, F4, 35) (dual of [65622, 65392, 36]-code), using
- construction X applied to C([0,17]) ⊂ C([0,12]) [i] based on
- linear OA(4209, 65537, F4, 35) (dual of [65537, 65328, 36]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,17], and minimum distance d ≥ |{−17,−16,…,17}|+1 = 36 (BCH-bound) [i]
- linear OA(4145, 65537, F4, 25) (dual of [65537, 65392, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(421, 85, F4, 9) (dual of [85, 64, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(421, 86, F4, 9) (dual of [86, 65, 10]-code), using
- construction X applied to C([0,17]) ⊂ C([0,12]) [i] based on
- linear OA(4230, 65624, F4, 34) (dual of [65624, 65394, 35]-code), using Gilbert–Varšamov bound and bm = 4230 > Vbs−1(k−1) = 583101 722473 790511 372997 199565 109025 548944 222921 190917 278975 837241 191020 263479 099347 303542 878423 165547 580590 859226 442418 987216 929015 567628 [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(4230, 65622, F4, 35) (dual of [65622, 65392, 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(4232, 32813, F4, 3, 35) (dual of [(32813, 3), 98207, 36]-NRT-code) | [i] | OOA Folding | |