Information on Result #682445
Linear OA(537, 78134, F5, 7) (dual of [78134, 78097, 8]-code), using construction X4 applied to Ce(6) ⊂ Ce(5) based on
- linear OA(536, 78125, F5, 7) (dual of [78125, 78089, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(529, 78125, F5, 6) (dual of [78125, 78096, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(58, 9, F5, 8) (dual of [9, 1, 9]-code or 9-arc in PG(7,5)), using
- dual of repetition code with length 9 [i]
- linear OA(51, 9, F5, 1) (dual of [9, 8, 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 OA(538, 78135, F5, 7) (dual of [78135, 78097, 8]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(537, 70201, F5, 2, 7) (dual of [(70201, 2), 140365, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(537, 70201, F5, 3, 7) (dual of [(70201, 3), 210566, 8]-NRT-code) | [i] | ||
| 4 | Digital (30, 37, 70201)-net over F5 | [i] | ||
| 5 | Linear OA(538, 78136, F5, 7) (dual of [78136, 78098, 8]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OOA(537, 39067, F5, 2, 7) (dual of [(39067, 2), 78097, 8]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(537, 26044, F5, 7, 7) (dual of [(26044, 7), 182271, 8]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |