Information on Result #709667
Linear OA(4245, 1042, F4, 65) (dual of [1042, 797, 66]-code), using construction XX applied to C1 = C([283,345]), C2 = C([281,342]), C3 = C1 + C2 = C([283,342]), and C∩ = C1 ∩ C2 = C([281,345]) based on
- linear OA(4236, 1023, F4, 63) (dual of [1023, 787, 64]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {283,284,…,345}, and designed minimum distance d ≥ |I|+1 = 64 [i]
- linear OA(4231, 1023, F4, 62) (dual of [1023, 792, 63]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {281,282,…,342}, and designed minimum distance d ≥ |I|+1 = 63 [i]
- linear OA(4241, 1023, F4, 65) (dual of [1023, 782, 66]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {281,282,…,345}, and designed minimum distance d ≥ |I|+1 = 66 [i]
- linear OA(4226, 1023, F4, 60) (dual of [1023, 797, 61]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {283,284,…,342}, and designed minimum distance d ≥ |I|+1 = 61 [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(41, 6, F4, 1) (dual of [6, 5, 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: 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(4245, 521, F4, 2, 65) (dual of [(521, 2), 797, 66]-NRT-code) | [i] | OOA Folding | |