Information on Result #710225
Linear OA(582, 136, F5, 40) (dual of [136, 54, 41]-code), using construction XX applied to C1 = C([123,36]), C2 = C([1,38]), C3 = C1 + C2 = C([1,36]), and C∩ = C1 ∩ C2 = C([123,38]) based on
- linear OA(574, 124, F5, 38) (dual of [124, 50, 39]-code), using the primitive BCH-code C(I) with length 124 = 53−1, defining interval I = {−1,0,…,36}, and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(576, 124, F5, 38) (dual of [124, 48, 39]-code), using the primitive narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(580, 124, F5, 40) (dual of [124, 44, 41]-code), using the primitive BCH-code C(I) with length 124 = 53−1, defining interval I = {−1,0,…,38}, and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(570, 124, F5, 36) (dual of [124, 54, 37]-code), using the primitive narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(51, 5, F5, 1) (dual of [5, 4, 2]-code), using
- Reed–Solomon code RS(4,5) [i]
- linear OA(51, 7, F5, 1) (dual of [7, 6, 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(583, 139, F5, 40) (dual of [139, 56, 41]-code) | [i] | Varšamov–Edel Lengthening | |
| 2 | Linear OOA(582, 68, F5, 2, 40) (dual of [(68, 2), 54, 41]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(582, 45, F5, 3, 40) (dual of [(45, 3), 53, 41]-NRT-code) | [i] | ||