Information on Result #710291
Linear OA(589, 136, F5, 44) (dual of [136, 47, 45]-code), using construction XX applied to C1 = C([21,62]), C2 = C([24,64]), C3 = C1 + C2 = C([24,62]), and C∩ = C1 ∩ C2 = C([21,64]) based on
- linear OA(580, 124, F5, 42) (dual of [124, 44, 43]-code), using the primitive BCH-code C(I) with length 124 = 53−1, defining interval I = {21,22,…,62}, and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(583, 124, F5, 41) (dual of [124, 41, 42]-code), using the primitive BCH-code C(I) with length 124 = 53−1, defining interval I = {24,25,…,64}, and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(586, 124, F5, 44) (dual of [124, 38, 45]-code), using the primitive BCH-code C(I) with length 124 = 53−1, defining interval I = {21,22,…,64}, and designed minimum distance d ≥ |I|+1 = 45 [i]
- linear OA(577, 124, F5, 39) (dual of [124, 47, 40]-code), using the primitive BCH-code C(I) with length 124 = 53−1, defining interval I = {24,25,…,62}, and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(52, 5, F5, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,5)), using
- Reed–Solomon code RS(3,5) [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 OOA(589, 68, F5, 2, 44) (dual of [(68, 2), 47, 45]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(589, 45, F5, 3, 44) (dual of [(45, 3), 46, 45]-NRT-code) | [i] | ||