Information on Result #1310362
Linear OA(527, 143, F5, 10) (dual of [143, 116, 11]-code), using 8 step Varšamov–Edel lengthening with (ri) = (1, 7 times 0) based on linear OA(526, 134, F5, 10) (dual of [134, 108, 11]-code), using
- construction XX applied to C1 = C([122,6]), C2 = C([0,7]), C3 = C1 + C2 = C([0,6]), and C∩ = C1 ∩ C2 = C([122,7]) [i] based on
- 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 = {−2,−1,…,6}, and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(519, 124, F5, 8) (dual of [124, 105, 9]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [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 = {−2,−1,…,7}, and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(516, 124, F5, 7) (dual of [124, 108, 8]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [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(527, 143, F5, 2, 10) (dual of [(143, 2), 259, 11]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(527, 143, F5, 3, 10) (dual of [(143, 3), 402, 11]-NRT-code) | [i] | ||
| 3 | Digital (17, 27, 143)-net over F5 | [i] | ||