Information on Result #709737
Linear OA(519, 136, F5, 7) (dual of [136, 117, 8]-code), using construction XX applied to C1 = C([26,31]), C2 = C([29,32]), C3 = C1 + C2 = C([29,31]), and C∩ = C1 ∩ C2 = C([26,32]) based on
- linear OA(513, 124, F5, 6) (dual of [124, 111, 7]-code), using the primitive BCH-code C(I) with length 124 = 53−1, defining interval I = {26,27,…,31}, and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(510, 124, F5, 4) (dual of [124, 114, 5]-code), using the primitive BCH-code C(I) with length 124 = 53−1, defining interval I = {29,30,31,32}, and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(516, 124, F5, 7) (dual of [124, 108, 8]-code), using the primitive BCH-code C(I) with length 124 = 53−1, defining interval I = {26,27,…,32}, and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(57, 124, F5, 3) (dual of [124, 117, 4]-code or 124-cap in PG(6,5)), using the primitive BCH-code C(I) with length 124 = 53−1, defining interval I = {29,30,31}, and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(53, 9, F5, 2) (dual of [9, 6, 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
- linear OA(50, 3, F5, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 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(519, 68, F5, 2, 7) (dual of [(68, 2), 117, 8]-NRT-code) | [i] | OOA Folding | |