Information on Result #1324278
Linear OA(4260, 65607, F4, 41) (dual of [65607, 65347, 42]-code), using construction X with Varšamov bound based on
- linear OA(4255, 65599, F4, 41) (dual of [65599, 65344, 42]-code), using
- construction X applied to C([0,20]) ⊂ C([0,16]) [i] based on
- linear OA(4241, 65537, F4, 41) (dual of [65537, 65296, 42]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,20], and minimum distance d ≥ |{−20,−19,…,20}|+1 = 42 (BCH-bound) [i]
- linear OA(4193, 65537, F4, 33) (dual of [65537, 65344, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(414, 62, F4, 7) (dual of [62, 48, 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([0,20]) ⊂ C([0,16]) [i] based on
- linear OA(4255, 65602, F4, 38) (dual of [65602, 65347, 39]-code), using Gilbert–Varšamov bound and bm = 4255 > Vbs−1(k−1) = 544 638530 026979 625254 010437 073021 020957 259235 678673 746597 176819 082196 406846 073111 833970 730405 871882 352035 117349 974261 159102 319082 112544 397352 286758 670732 [i]
- linear OA(42, 5, F4, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,4)), using
- extended Reed–Solomon code RSe(3,4) [i]
- Hamming code H(2,4) [i]
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(4260, 32803, F4, 2, 41) (dual of [(32803, 2), 65346, 42]-NRT-code) | [i] | OOA Folding | |