Information on Result #2277207
Linear OA(5111, 1953147, F5, 15) (dual of [1953147, 1953036, 16]-code), using 1 times code embedding in larger space based on linear OA(5110, 1953146, F5, 15) (dual of [1953146, 1953036, 16]-code), using
- construction X4 applied to C([0,7]) ⊂ C([0,6]) [i] based on
- linear OA(5109, 1953126, F5, 15) (dual of [1953126, 1953017, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 1953126 | 518−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(591, 1953126, F5, 13) (dual of [1953126, 1953035, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 1953126 | 518−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [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(5111, 1163334, F5, 2, 15) (dual of [(1163334, 2), 2326557, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5111, 1163334, F5, 3, 15) (dual of [(1163334, 3), 3489891, 16]-NRT-code) | [i] | ||
| 3 | Digital (96, 111, 1163334)-net over F5 | [i] | ||
| 4 | Linear OOA(5111, 651049, F5, 3, 15) (dual of [(651049, 3), 1953036, 16]-NRT-code) | [i] | OOA Folding | |