Information on Result #709761
Linear OA(521, 135, F5, 8) (dual of [135, 114, 9]-code), using construction XX applied to C1 = C([122,3]), C2 = C([0,5]), C3 = C1 + C2 = C([0,3]), and C∩ = C1 ∩ C2 = C([122,5]) based on
- linear OA(516, 124, F5, 6) (dual of [124, 108, 7]-code), using the primitive BCH-code C(I) with length 124 = 53−1, defining interval I = {−2,−1,…,3}, and designed minimum distance d ≥ |I|+1 = 7 [i]
- 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(519, 124, F5, 8) (dual of [124, 105, 9]-code), using the primitive BCH-code C(I) with length 124 = 53−1, defining interval I = {−2,−1,…,5}, and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(510, 124, F5, 4) (dual of [124, 114, 5]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(51, 7, F5, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(51, 4, F5, 1) (dual of [4, 3, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, 5, F5, 1) (dual of [5, 4, 2]-code), using
- Reed–Solomon code RS(4,5) [i]
- discarding factors / shortening the dual code based on linear OA(51, 5, F5, 1) (dual of [5, 4, 2]-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(521, 67, F5, 2, 8) (dual of [(67, 2), 113, 9]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(521, 45, F5, 3, 8) (dual of [(45, 3), 114, 9]-NRT-code) | [i] | ||