Information on Result #1324088
Linear OA(4212, 65607, F4, 33) (dual of [65607, 65395, 34]-code), using construction X with Varšamov bound based on
- linear OA(4207, 65599, F4, 33) (dual of [65599, 65392, 34]-code), using
- construction X applied to C([0,16]) ⊂ C([0,12]) [i] based on
- 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(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(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([0,16]) ⊂ C([0,12]) [i] based on
- linear OA(4207, 65602, F4, 30) (dual of [65602, 65395, 31]-code), using Gilbert–Varšamov bound and bm = 4207 > Vbs−1(k−1) = 378 230648 133154 475780 207693 252119 461232 352922 298145 706430 238006 436037 430799 117165 068569 623147 008411 713569 229202 748836 607412 [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 OA(4213, 65608, F4, 33) (dual of [65608, 65395, 34]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(4212, 32803, F4, 2, 33) (dual of [(32803, 2), 65394, 34]-NRT-code) | [i] | OOA Folding | |