Information on Result #710748
Linear OA(5124, 319, F5, 42) (dual of [319, 195, 43]-code), using construction XX applied to C1 = C([38,78]), C2 = C([40,79]), C3 = C1 + C2 = C([40,78]), and C∩ = C1 ∩ C2 = C([38,79]) based on
- linear OA(5119, 312, F5, 41) (dual of [312, 193, 42]-code), using the BCH-code C(I) with length 312 | 54−1, defining interval I = {38,39,…,78}, and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(5121, 312, F5, 40) (dual of [312, 191, 41]-code), using the BCH-code C(I) with length 312 | 54−1, defining interval I = {40,41,…,79}, and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(5123, 312, F5, 42) (dual of [312, 189, 43]-code), using the BCH-code C(I) with length 312 | 54−1, defining interval I = {38,39,…,79}, and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(5117, 312, F5, 39) (dual of [312, 195, 40]-code), using the BCH-code C(I) with length 312 | 54−1, defining interval I = {40,41,…,78}, and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(51, 3, F5, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, 5, F5, 1) (dual of [5, 4, 2]-code), using
- Reed–Solomon code RS(4,5) [i]
- discarding factors / shortening the dual code based on linear OA(51, 5, F5, 1) (dual of [5, 4, 2]-code), using
- linear OA(50, 4, F5, 0) (dual of [4, 4, 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: 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(5124, 159, F5, 2, 42) (dual of [(159, 2), 194, 43]-NRT-code) | [i] | OOA Folding | |