Information on Result #711578
Linear OA(5104, 659, F5, 30) (dual of [659, 555, 31]-code), using construction XX applied to C1 = C([130,156]), C2 = C([135,159]), C3 = C1 + C2 = C([135,156]), and C∩ = C1 ∩ C2 = C([130,159]) based on
- linear OA(583, 624, F5, 27) (dual of [624, 541, 28]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {130,131,…,156}, and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(581, 624, F5, 25) (dual of [624, 543, 26]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {135,136,…,159}, and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(595, 624, F5, 30) (dual of [624, 529, 31]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {130,131,…,159}, and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(569, 624, F5, 22) (dual of [624, 555, 23]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {135,136,…,156}, and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(56, 20, F5, 4) (dual of [20, 14, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(56, 30, F5, 4) (dual of [30, 24, 5]-code), using
- linear OA(53, 15, F5, 2) (dual of [15, 12, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(53, 24, F5, 2) (dual of [24, 21, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(53, 24, F5, 2) (dual of [24, 21, 3]-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(5104, 329, F5, 2, 30) (dual of [(329, 2), 554, 31]-NRT-code) | [i] | OOA Folding | |