Information on Result #1301912
Linear OA(5143, 390690, F5, 20) (dual of [390690, 390547, 21]-code), using construction X with Varšamov bound based on
- linear OA(5141, 390686, F5, 20) (dual of [390686, 390545, 21]-code), using
- construction X applied to C([0,10]) ⊂ C([0,6]) [i] based on
- linear OA(5129, 390626, F5, 21) (dual of [390626, 390497, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626 | 516−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(581, 390626, F5, 13) (dual of [390626, 390545, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626 | 516−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(512, 60, F5, 6) (dual of [60, 48, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(512, 62, F5, 6) (dual of [62, 50, 7]-code), using
- the cyclic code C(A) with length 62 | 53−1, defining set A = {4,8,11,17}, and minimum distance d ≥ |{8,11,14,…,23}|+1 = 7 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(512, 62, F5, 6) (dual of [62, 50, 7]-code), using
- construction X applied to C([0,10]) ⊂ C([0,6]) [i] based on
- linear OA(5141, 390688, F5, 19) (dual of [390688, 390547, 20]-code), using Gilbert–Varšamov bound and bm = 5141 > Vbs−1(k−1) = 482497 462900 091841 739377 257396 389014 135003 942578 884340 096741 576554 978731 179412 575625 261667 163725 [i]
- linear OA(50, 2, F5, 0) (dual of [2, 2, 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(5143, 390690, F5, 2, 20) (dual of [(390690, 2), 781237, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5143, 390690, F5, 3, 20) (dual of [(390690, 3), 1171927, 21]-NRT-code) | [i] | ||
| 3 | Digital (123, 143, 390690)-net over F5 | [i] | ||
| 4 | Linear OOA(5143, 195345, F5, 2, 20) (dual of [(195345, 2), 390547, 21]-NRT-code) | [i] | OOA Folding | |