Information on Result #682511
Linear OA(5125, 78172, F5, 21) (dual of [78172, 78047, 22]-code), using construction X applied to Ce(20) ⊂ Ce(13) based on
- linear OA(5113, 78125, F5, 21) (dual of [78125, 78012, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(578, 78125, F5, 14) (dual of [78125, 78047, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(512, 47, F5, 6) (dual of [47, 35, 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(5126, 78173, F5, 21) (dual of [78173, 78047, 22]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(5124, 78171, F5, 20) (dual of [78171, 78047, 21]-code) | [i] | Truncation | |
| 3 | Linear OA(5126, 78174, F5, 21) (dual of [78174, 78048, 22]-code) | [i] | Construction X with Varšamov Bound | |
| 4 | Linear OOA(5125, 39086, F5, 2, 21) (dual of [(39086, 2), 78047, 22]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(5125, 26057, F5, 3, 21) (dual of [(26057, 3), 78046, 22]-NRT-code) | [i] | ||
| 6 | Linear OOA(5125, 7817, F5, 21, 21) (dual of [(7817, 21), 164032, 22]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |