Information on Result #711650
Linear OA(5119, 674, F5, 33) (dual of [674, 555, 34]-code), using construction XX applied to C1 = C([129,157]), C2 = C([136,161]), C3 = C1 + C2 = C([136,157]), and C∩ = C1 ∩ C2 = C([129,161]) based on
- linear OA(591, 624, F5, 29) (dual of [624, 533, 30]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {129,130,…,157}, and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(581, 624, F5, 26) (dual of [624, 543, 27]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {136,137,…,161}, and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(5103, 624, F5, 33) (dual of [624, 521, 34]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {129,130,…,161}, and designed minimum distance d ≥ |I|+1 = 34 [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 = {136,137,…,157}, and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(512, 34, F5, 6) (dual of [34, 22, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(512, 62, F5, 6) (dual of [62, 50, 7]-code), using
- the cyclic code C(A) with length 62 | 53−1, defining set A = {4,8,11,17}, and minimum distance d ≥ |{8,11,14,…,23}|+1 = 7 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(512, 62, F5, 6) (dual of [62, 50, 7]-code), using
- linear OA(54, 16, F5, 3) (dual of [16, 12, 4]-code or 16-cap in PG(3,5)), 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(5119, 337, F5, 2, 33) (dual of [(337, 2), 555, 34]-NRT-code) | [i] | OOA Folding | |