Information on Result #709727
Linear OA(518, 133, F5, 7) (dual of [133, 115, 8]-code), using construction XX applied to C1 = C([0,5]), C2 = C([3,6]), C3 = C1 + C2 = C([3,5]), and C∩ = C1 ∩ C2 = C([0,6]) based on
- linear OA(513, 124, F5, 6) (dual of [124, 111, 7]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(512, 124, F5, 4) (dual of [124, 112, 5]-code), using the primitive BCH-code C(I) with length 124 = 53−1, defining interval I = {3,4,5,6}, and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(516, 124, F5, 7) (dual of [124, 108, 8]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(59, 124, F5, 3) (dual of [124, 115, 4]-code or 124-cap in PG(8,5)), using the primitive BCH-code C(I) with length 124 = 53−1, defining interval I = {3,4,5}, and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(52, 6, F5, 2) (dual of [6, 4, 3]-code or 6-arc in PG(1,5)), using
- extended Reed–Solomon code RSe(4,5) [i]
- Hamming code H(2,5) [i]
- 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(518, 66, F5, 2, 7) (dual of [(66, 2), 114, 8]-NRT-code) | [i] | OOA Folding | |