Information on Result #737472
Linear OA(5144, 390689, F5, 21) (dual of [390689, 390545, 22]-code), using construction X applied to C([0,10]) ⊂ C([0,6]) based on
- linear OA(5129, 390626, F5, 21) (dual of [390626, 390497, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626 | 516−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(581, 390626, F5, 13) (dual of [390626, 390545, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626 | 516−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(515, 63, F5, 7) (dual of [63, 48, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(515, 65, F5, 7) (dual of [65, 50, 8]-code), using
- construction X applied to C({1,4,8,11,17}) ⊂ C({4,8,11,17}) [i] based on
- linear OA(515, 62, F5, 7) (dual of [62, 47, 8]-code), using the cyclic code C(A) with length 62 | 53−1, defining set A = {1,4,8,11,17}, and minimum distance d ≥ |{5,8,11,…,23}|+1 = 8 (BCH-bound) [i]
- 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]
- linear OA(50, 3, F5, 0) (dual of [3, 3, 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
- construction X applied to C({1,4,8,11,17}) ⊂ C({4,8,11,17}) [i] based on
- discarding factors / shortening the dual code based on linear OA(515, 65, F5, 7) (dual of [65, 50, 8]-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(5143, 390688, F5, 20) (dual of [390688, 390545, 21]-code) | [i] | Truncation | |