Information on Result #683901
Linear OA(543, 315, F5, 14) (dual of [315, 272, 15]-code), using construction X applied to Ce(13) ⊂ Ce(12) based on
- linear OA(543, 313, F5, 14) (dual of [313, 270, 15]-code), using an extension Ce(13) of the narrow-sense BCH-code C(I) with length 312 | 54−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(541, 313, F5, 13) (dual of [313, 272, 14]-code), using an extension Ce(12) of the narrow-sense BCH-code C(I) with length 312 | 54−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [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: 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 OOA(543, 315, F5, 2, 14) (dual of [(315, 2), 587, 15]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(543, 315, F5, 3, 14) (dual of [(315, 3), 902, 15]-NRT-code) | [i] | ||
| 3 | Digital (29, 43, 315)-net over F5 | [i] | ||
| 4 | Linear OA(544, 341, F5, 14) (dual of [341, 297, 15]-code) | [i] | Varšamov–Edel Lengthening | |
| 5 | Linear OOA(543, 157, F5, 2, 14) (dual of [(157, 2), 271, 15]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(543, 105, F5, 3, 14) (dual of [(105, 3), 272, 15]-NRT-code) | [i] | ||