Information on Result #707448
Linear OA(424, 1041, F4, 6) (dual of [1041, 1017, 7]-code), using construction XX applied to C1 = C([337,341]), C2 = C([340,342]), C3 = C1 + C2 = C([340,341]), and C∩ = C1 ∩ C2 = C([337,342]) based on
- linear OA(416, 1023, F4, 5) (dual of [1023, 1007, 6]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {337,338,339,340,341}, and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(411, 1023, F4, 3) (dual of [1023, 1012, 4]-code or 1023-cap in PG(10,4)), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {340,341,342}, and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(421, 1023, F4, 6) (dual of [1023, 1002, 7]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {337,338,…,342}, and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(46, 1023, F4, 2) (dual of [1023, 1017, 3]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {340,341}, and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(43, 13, F4, 2) (dual of [13, 10, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- Hamming code H(3,4) [i]
- discarding factors / shortening the dual code based on linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- linear OA(40, 5, F4, 0) (dual of [5, 5, 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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(424, 520, F4, 2, 6) (dual of [(520, 2), 1016, 7]-NRT-code) | [i] | OOA Folding | |