Information on Result #1310457
Linear OA(541, 176, F5, 15) (dual of [176, 135, 16]-code), using 42 step Varšamov–Edel lengthening with (ri) = (1, 0, 0, 1, 7 times 0, 1, 13 times 0, 1, 16 times 0) based on linear OA(537, 130, F5, 15) (dual of [130, 93, 16]-code), using
- construction XX applied to C1 = C([123,12]), C2 = C([0,13]), C3 = C1 + C2 = C([0,12]), and C∩ = C1 ∩ C2 = C([123,13]) [i] based on
- linear OA(534, 124, F5, 14) (dual of [124, 90, 15]-code), using the primitive BCH-code C(I) with length 124 = 53−1, defining interval I = {−1,0,…,12}, and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(534, 124, F5, 14) (dual of [124, 90, 15]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(537, 124, F5, 15) (dual of [124, 87, 16]-code), using the primitive BCH-code C(I) with length 124 = 53−1, defining interval I = {−1,0,…,13}, and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(531, 124, F5, 13) (dual of [124, 93, 14]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [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
- linear OA(50, 3, F5, 0) (dual of [3, 3, 1]-code) (see above)
Mode: 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(541, 176, F5, 2, 15) (dual of [(176, 2), 311, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(541, 176, F5, 3, 15) (dual of [(176, 3), 487, 16]-NRT-code) | [i] | ||
| 3 | Digital (26, 41, 176)-net over F5 | [i] | ||