Information on Result #709630
Linear OA(4240, 1047, F4, 63) (dual of [1047, 807, 64]-code), using construction XX applied to C1 = C([285,345]), C2 = C([283,342]), C3 = C1 + C2 = C([285,342]), and C∩ = C1 ∩ C2 = C([283,345]) based on
- linear OA(4226, 1023, F4, 61) (dual of [1023, 797, 62]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {285,286,…,345}, and designed minimum distance d ≥ |I|+1 = 62 [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(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(4216, 1023, F4, 58) (dual of [1023, 807, 59]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {285,286,…,342}, and designed minimum distance d ≥ |I|+1 = 59 [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, 11, F4, 1) (dual of [11, 10, 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(4240, 523, F4, 2, 63) (dual of [(523, 2), 806, 64]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(4240, 349, F4, 3, 63) (dual of [(349, 3), 807, 64]-NRT-code) | [i] | ||