Information on Result #2277153
Linear OA(5102, 1953146, F5, 14) (dual of [1953146, 1953044, 15]-code), using 1 times code embedding in larger space based on linear OA(5101, 1953145, F5, 14) (dual of [1953145, 1953044, 15]-code), using
- construction X4 applied to Ce(13) ⊂ Ce(11) [i] based on
- linear OA(5100, 1953125, F5, 14) (dual of [1953125, 1953025, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(582, 1953125, F5, 12) (dual of [1953125, 1953043, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(519, 20, F5, 19) (dual of [20, 1, 20]-code or 20-arc in PG(18,5)), using
- dual of repetition code with length 20 [i]
- linear OA(51, 20, F5, 1) (dual of [20, 19, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-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(5102, 1009940, F5, 2, 14) (dual of [(1009940, 2), 2019778, 15]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5102, 1009940, F5, 3, 14) (dual of [(1009940, 3), 3029718, 15]-NRT-code) | [i] | ||
| 3 | Digital (88, 102, 1009940)-net over F5 | [i] | ||
| 4 | Linear OOA(5102, 976573, F5, 2, 14) (dual of [(976573, 2), 1953044, 15]-NRT-code) | [i] | OOA Folding | |