Information on Result #682523
Linear OA(5111, 78179, F5, 18) (dual of [78179, 78068, 19]-code), using construction X applied to Ce(17) ⊂ Ce(10) based on
- linear OA(599, 78125, F5, 18) (dual of [78125, 78026, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(557, 78125, F5, 11) (dual of [78125, 78068, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(512, 54, F5, 6) (dual of [54, 42, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(512, 62, F5, 6) (dual of [62, 50, 7]-code), using
- the cyclic code C(A) with length 62 | 53−1, defining set A = {4,8,11,17}, and minimum distance d ≥ |{8,11,14,…,23}|+1 = 7 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(512, 62, F5, 6) (dual of [62, 50, 7]-code), 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(5112, 78180, F5, 18) (dual of [78180, 78068, 19]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(5111, 78179, F5, 2, 18) (dual of [(78179, 2), 156247, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(5111, 78179, F5, 3, 18) (dual of [(78179, 3), 234426, 19]-NRT-code) | [i] | ||
| 4 | Digital (93, 111, 78179)-net over F5 | [i] | ||
| 5 | Linear OA(5112, 78181, F5, 18) (dual of [78181, 78069, 19]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OOA(5111, 39089, F5, 2, 18) (dual of [(39089, 2), 78067, 19]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(5111, 26059, F5, 3, 18) (dual of [(26059, 3), 78066, 19]-NRT-code) | [i] | ||
| 8 | Linear OOA(5111, 8686, F5, 18, 18) (dual of [(8686, 18), 156237, 19]-NRT-code) | [i] | OA Folding and Stacking | |