Information on Result #704445
Linear OA(3110, 759, F3, 26) (dual of [759, 649, 27]-code), using construction XX applied to C1 = C([340,364]), C2 = C([345,365]), C3 = C1 + C2 = C([345,364]), and C∩ = C1 ∩ C2 = C([340,365]) based on
- linear OA(397, 728, F3, 25) (dual of [728, 631, 26]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {340,341,…,364}, and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(385, 728, F3, 21) (dual of [728, 643, 22]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {345,346,…,365}, and designed minimum distance d ≥ |I|+1 = 22 [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 = {340,341,…,365}, and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(379, 728, F3, 20) (dual of [728, 649, 21]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {345,346,…,364}, and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(37, 25, F3, 4) (dual of [25, 18, 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(3110, 699, F3, 2, 26) (dual of [(699, 2), 1288, 27]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3110, 699, F3, 3, 26) (dual of [(699, 3), 1987, 27]-NRT-code) | [i] | ||
| 3 | Linear OOA(3110, 699, F3, 4, 26) (dual of [(699, 4), 2686, 27]-NRT-code) | [i] | ||
| 4 | Linear OOA(3110, 699, F3, 5, 26) (dual of [(699, 5), 3385, 27]-NRT-code) | [i] | ||
| 5 | Digital (84, 110, 699)-net over F3 | [i] | ||
| 6 | Linear OOA(3110, 379, F3, 2, 26) (dual of [(379, 2), 648, 27]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3110, 253, F3, 3, 26) (dual of [(253, 3), 649, 27]-NRT-code) | [i] | ||