Information on Result #704440
Linear OA(3123, 780, F3, 27) (dual of [780, 657, 28]-code), using construction XX applied to C1 = C([349,371]), C2 = C([345,365]), C3 = C1 + C2 = C([349,365]), and C∩ = C1 ∩ C2 = C([345,371]) based on
- linear OA(391, 728, F3, 23) (dual of [728, 637, 24]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {349,350,…,371}, and designed minimum distance d ≥ |I|+1 = 24 [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(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 = {345,346,…,371}, and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(367, 728, F3, 17) (dual of [728, 661, 18]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {349,350,…,365}, and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(38, 28, F3, 5) (dual of [28, 20, 6]-code), using
- dual code (with bound on d by construction Y1) [i] based on
- linear OA(36, 24, F3, 3) (dual of [24, 18, 4]-code or 24-cap in PG(5,3)), using
- discarding factors / shortening the dual code based on linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), 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(3123, 390, F3, 2, 27) (dual of [(390, 2), 657, 28]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(3123, 260, F3, 3, 27) (dual of [(260, 3), 657, 28]-NRT-code) | [i] | ||