Information on Result #709843
Linear OA(533, 135, F5, 13) (dual of [135, 102, 14]-code), using construction XX applied to C1 = C([122,8]), C2 = C([0,10]), C3 = C1 + C2 = C([0,8]), and C∩ = C1 ∩ C2 = C([122,10]) based on
- linear OA(528, 124, F5, 11) (dual of [124, 96, 12]-code), using the primitive BCH-code C(I) with length 124 = 53−1, defining interval I = {−2,−1,…,8}, and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(525, 124, F5, 11) (dual of [124, 99, 12]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(531, 124, F5, 13) (dual of [124, 93, 14]-code), using the primitive BCH-code C(I) with length 124 = 53−1, defining interval I = {−2,−1,…,10}, and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(522, 124, F5, 9) (dual of [124, 102, 10]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [0,8], and designed minimum distance d ≥ |I|+1 = 10 [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(533, 126, F5, 2, 13) (dual of [(126, 2), 219, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(533, 126, F5, 3, 13) (dual of [(126, 3), 345, 14]-NRT-code) | [i] | ||
| 3 | Digital (20, 33, 126)-net over F5 | [i] | ||
| 4 | Linear OOA(533, 67, F5, 2, 13) (dual of [(67, 2), 101, 14]-NRT-code) | [i] | OOA Folding | |