Information on Result #682333
Linear OA(5141, 390677, F5, 21) (dual of [390677, 390536, 22]-code), using construction X applied to Ce(20) ⊂ Ce(13) based on
- linear OA(5129, 390625, F5, 21) (dual of [390625, 390496, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(589, 390625, F5, 14) (dual of [390625, 390536, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(512, 52, F5, 6) (dual of [52, 40, 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
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 OA(5142, 390678, F5, 21) (dual of [390678, 390536, 22]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(5143, 390679, F5, 21) (dual of [390679, 390536, 22]-code) | [i] | ||
| 3 | Linear OA(5140, 390676, F5, 20) (dual of [390676, 390536, 21]-code) | [i] | Truncation | |
| 4 | Linear OA(5143, 390680, F5, 21) (dual of [390680, 390537, 22]-code) | [i] | Construction X with Varšamov Bound | |
| 5 | Linear OOA(5141, 195338, F5, 2, 21) (dual of [(195338, 2), 390535, 22]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(5141, 130225, F5, 3, 21) (dual of [(130225, 3), 390534, 22]-NRT-code) | [i] | ||
| 7 | Linear OOA(5141, 39067, F5, 21, 21) (dual of [(39067, 21), 820266, 22]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |