Information on Result #709059
Linear OA(4185, 1042, F4, 49) (dual of [1042, 857, 50]-code), using construction XX applied to C1 = C([299,345]), C2 = C([297,342]), C3 = C1 + C2 = C([299,342]), and C∩ = C1 ∩ C2 = C([297,345]) based on
- linear OA(4176, 1023, F4, 47) (dual of [1023, 847, 48]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {299,300,…,345}, and designed minimum distance d ≥ |I|+1 = 48 [i]
- linear OA(4171, 1023, F4, 46) (dual of [1023, 852, 47]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {297,298,…,342}, and designed minimum distance d ≥ |I|+1 = 47 [i]
- linear OA(4181, 1023, F4, 49) (dual of [1023, 842, 50]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {297,298,…,345}, and designed minimum distance d ≥ |I|+1 = 50 [i]
- linear OA(4166, 1023, F4, 44) (dual of [1023, 857, 45]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {299,300,…,342}, and designed minimum distance d ≥ |I|+1 = 45 [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(4185, 521, F4, 2, 49) (dual of [(521, 2), 857, 50]-NRT-code) | [i] | OOA Folding | |