Information on Result #701138
Linear OA(426, 89, F4, 10) (dual of [89, 63, 11]-code), using construction X applied to C({2,5,6,7,14,17,21}) ⊂ C({2,5,6,14,17,21}) based on
- linear OA(426, 85, F4, 10) (dual of [85, 59, 11]-code), using the cyclic code C(A) with length 85 | 44−1, defining set A = {2,5,6,7,14,17,21}, and minimum distance d ≥ |{−4,−1,2,…,23}|+1 = 11 (BCH-bound) [i]
- linear OA(422, 85, F4, 9) (dual of [85, 63, 10]-code), using the cyclic code C(A) with length 85 | 44−1, defining set A = {2,5,6,14,17,21}, and minimum distance d ≥ |{−4,−1,2,…,20}|+1 = 10 (BCH-bound) [i]
- linear OA(40, 4, F4, 0) (dual of [4, 4, 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
Mode: Constructive and 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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(427, 97, F4, 10) (dual of [97, 70, 11]-code) | [i] | Varšamov–Edel Lengthening | |
| 2 | Linear OA(428, 109, F4, 10) (dual of [109, 81, 11]-code) | [i] | ||
| 3 | Linear OA(4251, 65625, F4, 38) (dual of [65625, 65374, 39]-code) | [i] | Construction X with Extended Narrow-Sense BCH Codes | |
| 4 | Linear OA(4243, 65625, F4, 37) (dual of [65625, 65382, 38]-code) | [i] | ||
| 5 | Linear OA(4258, 16473, F4, 44) (dual of [16473, 16215, 45]-code) | [i] | ||
| 6 | Linear OA(4237, 16473, F4, 40) (dual of [16473, 16236, 41]-code) | [i] | ||
| 7 | Linear OOA(426, 44, F4, 2, 10) (dual of [(44, 2), 62, 11]-NRT-code) | [i] | OOA Folding | |