Information on Result #703971
Linear OA(3131, 386, F3, 35) (dual of [386, 255, 36]-code), using construction XX applied to C1 = C([167,200]), C2 = C([166,197]), C3 = C1 + C2 = C([167,197]), and C∩ = C1 ∩ C2 = C([166,200]) based on
- linear OA(3121, 364, F3, 34) (dual of [364, 243, 35]-code), using the BCH-code C(I) with length 364 | 36−1, defining interval I = {167,168,…,200}, and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(3115, 364, F3, 32) (dual of [364, 249, 33]-code), using the BCH-code C(I) with length 364 | 36−1, defining interval I = {166,167,…,197}, and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(3127, 364, F3, 35) (dual of [364, 237, 36]-code), using the BCH-code C(I) with length 364 | 36−1, defining interval I = {166,167,…,200}, and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(3109, 364, F3, 31) (dual of [364, 255, 32]-code), using the BCH-code C(I) with length 364 | 36−1, defining interval I = {167,168,…,197}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(34, 16, F3, 2) (dual of [16, 12, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- Hamming code H(4,3) [i]
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- linear OA(30, 6, F3, 0) (dual of [6, 6, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 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 OA(3132, 387, F3, 35) (dual of [387, 255, 36]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(3131, 193, F3, 2, 35) (dual of [(193, 2), 255, 36]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(3131, 128, F3, 3, 35) (dual of [(128, 3), 253, 36]-NRT-code) | [i] | ||