Information on Result #704960
Linear OA(3170, 788, F3, 39) (dual of [788, 618, 40]-code), using construction XX applied to C1 = C([361,394]), C2 = C([355,388]), C3 = C1 + C2 = C([361,388]), and C∩ = C1 ∩ C2 = C([355,394]) based on
- linear OA(3130, 728, F3, 34) (dual of [728, 598, 35]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {361,362,…,394}, and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(3133, 728, F3, 34) (dual of [728, 595, 35]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {355,356,…,388}, and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(3154, 728, F3, 40) (dual of [728, 574, 41]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {355,356,…,394}, and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(3109, 728, F3, 28) (dual of [728, 619, 29]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {361,362,…,388}, and designed minimum distance d ≥ |I|+1 = 29 [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(38, 32, F3, 4) (dual of [32, 24, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-code), using
- the narrow-sense BCH-code C(I) with length 41 | 38−1, defining interval I = [1,1], and minimum distance d ≥ |{−3,−1,1,3}|+1 = 5 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-code), 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(3170, 394, F3, 2, 39) (dual of [(394, 2), 618, 40]-NRT-code) | [i] | OOA Folding | |