Information on Result #682828
Linear OA(591, 15651, F5, 18) (dual of [15651, 15560, 19]-code), using construction XX applied to Ce(17) ⊂ Ce(13) ⊂ Ce(12) based on
- linear OA(585, 15625, F5, 18) (dual of [15625, 15540, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(567, 15625, F5, 14) (dual of [15625, 15558, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(561, 15625, F5, 13) (dual of [15625, 15564, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(54, 24, F5, 3) (dual of [24, 20, 4]-code or 24-cap in PG(3,5)), using
- 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(591, 14516, F5, 2, 18) (dual of [(14516, 2), 28941, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(591, 14516, F5, 3, 18) (dual of [(14516, 3), 43457, 19]-NRT-code) | [i] | ||
| 3 | Digital (73, 91, 14516)-net over F5 | [i] | ||
| 4 | Linear OOA(591, 1739, F5, 18, 18) (dual of [(1739, 18), 31211, 19]-NRT-code) | [i] | OA Folding and Stacking | |