Information on Result #707316
Linear OA(4172, 353, F4, 53) (dual of [353, 181, 54]-code), using construction XX applied to C1 = C([65,115]), C2 = C([63,113]), C3 = C1 + C2 = C([65,113]), and C∩ = C1 ∩ C2 = C([63,115]) based on
- linear OA(4165, 341, F4, 51) (dual of [341, 176, 52]-code), using the BCH-code C(I) with length 341 | 45−1, defining interval I = {65,66,…,115}, and designed minimum distance d ≥ |I|+1 = 52 [i]
- linear OA(4165, 341, F4, 51) (dual of [341, 176, 52]-code), using the BCH-code C(I) with length 341 | 45−1, defining interval I = {63,64,…,113}, and designed minimum distance d ≥ |I|+1 = 52 [i]
- linear OA(4170, 341, F4, 53) (dual of [341, 171, 54]-code), using the BCH-code C(I) with length 341 | 45−1, defining interval I = {63,64,…,115}, and designed minimum distance d ≥ |I|+1 = 54 [i]
- linear OA(4160, 341, F4, 49) (dual of [341, 181, 50]-code), using the BCH-code C(I) with length 341 | 45−1, defining interval I = {65,66,…,113}, and designed minimum distance d ≥ |I|+1 = 50 [i]
- 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
- linear OA(41, 6, F4, 1) (dual of [6, 5, 2]-code) (see above)
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(4172, 176, F4, 2, 53) (dual of [(176, 2), 180, 54]-NRT-code) | [i] | OOA Folding | |