Information on Result #1308825
Linear OA(4232, 4145, F4, 51) (dual of [4145, 3913, 52]-code), using 33 step Varšamov–Edel lengthening with (ri) = (1, 7 times 0, 1, 24 times 0) based on linear OA(4230, 4110, F4, 51) (dual of [4110, 3880, 52]-code), using
- construction X applied to C([0,25]) ⊂ C([0,24]) [i] based on
- linear OA(4229, 4097, F4, 51) (dual of [4097, 3868, 52]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 412−1, defining interval I = [0,25], and minimum distance d ≥ |{−25,−24,…,25}|+1 = 52 (BCH-bound) [i]
- linear OA(4217, 4097, F4, 49) (dual of [4097, 3880, 50]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 412−1, defining interval I = [0,24], and minimum distance d ≥ |{−24,−23,…,24}|+1 = 50 (BCH-bound) [i]
- linear OA(41, 13, F4, 1) (dual of [13, 12, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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, 4145, F4, 2, 51) (dual of [(4145, 2), 8058, 52]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4232, 4145, F4, 3, 51) (dual of [(4145, 3), 12203, 52]-NRT-code) | [i] | ||
| 3 | Digital (181, 232, 4145)-net over F4 | [i] | ||
| 4 | Linear OOA(4232, 2072, F4, 2, 51) (dual of [(2072, 2), 3912, 52]-NRT-code) | [i] | OOA Folding | |