Information on Result #709808
Linear OA(531, 136, F5, 12) (dual of [136, 105, 13]-code), using construction XX applied to C1 = C([21,31]), C2 = C([24,32]), C3 = C1 + C2 = C([24,31]), 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(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 = {24,25,…,32}, and designed minimum distance d ≥ |I|+1 = 10 [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(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 = {24,25,…,31}, and designed minimum distance d ≥ |I|+1 = 9 [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(531, 136, F5, 2, 12) (dual of [(136, 2), 241, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(531, 136, F5, 3, 12) (dual of [(136, 3), 377, 13]-NRT-code) | [i] | ||
| 3 | Digital (19, 31, 136)-net over F5 | [i] | ||
| 4 | Linear OOA(531, 68, F5, 2, 12) (dual of [(68, 2), 105, 13]-NRT-code) | [i] | OOA Folding | |