Information on Result #1301825
Linear OA(5127, 15657, F5, 25) (dual of [15657, 15530, 26]-code), using construction X with Varšamov bound based on
- linear OA(5126, 15655, F5, 25) (dual of [15655, 15529, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,10]) [i] based on
- linear OA(5121, 15626, F5, 25) (dual of [15626, 15505, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 512−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(597, 15626, F5, 21) (dual of [15626, 15529, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 512−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(55, 29, F5, 3) (dual of [29, 24, 4]-code or 29-cap in PG(4,5)), using
- discarding factors / shortening the dual code based on linear OA(55, 42, F5, 3) (dual of [42, 37, 4]-code or 42-cap in PG(4,5)), using
- construction X applied to C([0,12]) ⊂ C([0,10]) [i] based on
- linear OA(5126, 15656, F5, 24) (dual of [15656, 15530, 25]-code), using Gilbert–Varšamov bound and bm = 5126 > Vbs−1(k−1) = 8036 071774 602501 695893 453153 665610 687959 611549 162862 024034 630845 201558 654492 812811 986605 [i]
- linear OA(50, 1, F5, 0) (dual of [1, 1, 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: 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(5127, 15657, F5, 2, 25) (dual of [(15657, 2), 31187, 26]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5127, 15657, F5, 3, 25) (dual of [(15657, 3), 46844, 26]-NRT-code) | [i] | ||
| 3 | Digital (102, 127, 15657)-net over F5 | [i] | ||