Information on Result #1310433
Linear OA(538, 164, F5, 14) (dual of [164, 126, 15]-code), using 27 step Varšamov–Edel lengthening with (ri) = (1, 0, 0, 1, 8 times 0, 1, 14 times 0) based on linear OA(535, 134, F5, 14) (dual of [134, 99, 15]-code), using
- construction XX applied to C1 = C([122,10]), C2 = C([0,11]), C3 = C1 + C2 = C([0,10]), and C∩ = C1 ∩ C2 = C([122,11]) [i] based on
- 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(528, 124, F5, 12) (dual of [124, 96, 13]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- 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 = {−2,−1,…,11}, and designed minimum distance d ≥ |I|+1 = 15 [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(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(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: 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(538, 164, F5, 2, 14) (dual of [(164, 2), 290, 15]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(538, 164, F5, 3, 14) (dual of [(164, 3), 454, 15]-NRT-code) | [i] | ||
| 3 | Digital (24, 38, 164)-net over F5 | [i] | ||