Information on Result #709824
Linear OA(529, 131, F5, 12) (dual of [131, 102, 13]-code), using construction XX applied to C1 = C([21,31]), C2 = C([23,32]), C3 = C1 + C2 = C([23,31]), and C∩ = C1 ∩ C2 = C([21,32]) based on
- linear OA(525, 124, F5, 11) (dual of [124, 99, 12]-code), using the primitive BCH-code C(I) with length 124 = 53−1, defining interval I = {21,22,…,31}, and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(525, 124, F5, 10) (dual of [124, 99, 11]-code), using the primitive BCH-code C(I) with length 124 = 53−1, defining interval I = {23,24,…,32}, and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(528, 124, F5, 12) (dual of [124, 96, 13]-code), using the primitive BCH-code C(I) with length 124 = 53−1, defining interval I = {21,22,…,32}, and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(522, 124, F5, 9) (dual of [124, 102, 10]-code), using the primitive BCH-code C(I) with length 124 = 53−1, defining interval I = {23,24,…,31}, and designed minimum distance d ≥ |I|+1 = 10 [i]
- 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
- 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(529, 97, F5, 2, 12) (dual of [(97, 2), 165, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(529, 97, F5, 3, 12) (dual of [(97, 3), 262, 13]-NRT-code) | [i] | ||
| 3 | Digital (17, 29, 97)-net over F5 | [i] | ||
| 4 | Linear OOA(529, 65, F5, 2, 12) (dual of [(65, 2), 101, 13]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(529, 43, F5, 3, 12) (dual of [(43, 3), 100, 13]-NRT-code) | [i] | ||