Information on Result #704607
Linear OA(3131, 756, F3, 32) (dual of [756, 625, 33]-code), using construction XX applied to C1 = C([334,364]), C2 = C([339,365]), C3 = C1 + C2 = C([339,364]), and C∩ = C1 ∩ C2 = C([334,365]) based on
- linear OA(3118, 728, F3, 31) (dual of [728, 610, 32]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {334,335,…,364}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(3109, 728, F3, 27) (dual of [728, 619, 28]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {339,340,…,365}, and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(3124, 728, F3, 32) (dual of [728, 604, 33]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {334,335,…,365}, and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(3103, 728, F3, 26) (dual of [728, 625, 27]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {339,340,…,364}, and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(37, 22, F3, 4) (dual of [22, 15, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(37, 26, F3, 4) (dual of [26, 19, 5]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 26 = 33−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(37, 26, F3, 4) (dual of [26, 19, 5]-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 OOA(3131, 677, F3, 2, 32) (dual of [(677, 2), 1223, 33]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3131, 677, F3, 3, 32) (dual of [(677, 3), 1900, 33]-NRT-code) | [i] | ||
| 3 | Linear OOA(3131, 677, F3, 4, 32) (dual of [(677, 4), 2577, 33]-NRT-code) | [i] | ||
| 4 | Linear OOA(3131, 677, F3, 5, 32) (dual of [(677, 5), 3254, 33]-NRT-code) | [i] | ||
| 5 | Digital (99, 131, 677)-net over F3 | [i] | ||
| 6 | Linear OOA(3131, 378, F3, 2, 32) (dual of [(378, 2), 625, 33]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3131, 252, F3, 3, 32) (dual of [(252, 3), 625, 33]-NRT-code) | [i] | ||
| 8 | Linear OOA(3131, 189, F3, 4, 32) (dual of [(189, 4), 625, 33]-NRT-code) | [i] | ||