Information on Result #1431687
Linear OOA(4227, 16446, F4, 2, 40) (dual of [(16446, 2), 32665, 41]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(4227, 16446, F4, 40) (dual of [16446, 16219, 41]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(4224, 16440, F4, 40) (dual of [16440, 16216, 41]-code), using
- construction X applied to C([0,20]) ⊂ C([0,16]) [i] based on
- linear OA(4211, 16385, F4, 41) (dual of [16385, 16174, 42]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,20], and minimum distance d ≥ |{−20,−19,…,20}|+1 = 42 (BCH-bound) [i]
- linear OA(4169, 16385, F4, 33) (dual of [16385, 16216, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(413, 55, F4, 6) (dual of [55, 42, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- discarding factors / shortening the dual code based on linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-code), using
- construction X applied to C([0,20]) ⊂ C([0,16]) [i] based on
- linear OA(4224, 16443, F4, 39) (dual of [16443, 16219, 40]-code), using Gilbert–Varšamov bound and bm = 4224 > Vbs−1(k−1) = 39 821365 238914 168531 951313 719462 111168 843573 725219 539111 694287 426719 268487 085353 314936 884335 370330 497102 072402 578233 559990 809587 789556 [i]
- linear OA(40, 3, F4, 0) (dual of [3, 3, 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(4224, 16440, F4, 40) (dual of [16440, 16216, 41]-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(4227, 8223, F4, 3, 40) (dual of [(8223, 3), 24442, 41]-NRT-code) | [i] | OOA Folding | |