Information on Result #731010
Linear OA(5146, 1262, F5, 38) (dual of [1262, 1116, 39]-code), using trace code based on linear OA(2573, 631, F25, 38) (dual of [631, 558, 39]-code), using
- construction XX applied to C1 = C([622,34]), C2 = C([0,35]), C3 = C1 + C2 = C([0,34]), and C∩ = C1 ∩ C2 = C([622,35]) [i] based on
- linear OA(2570, 624, F25, 37) (dual of [624, 554, 38]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−2,−1,…,34}, and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(2568, 624, F25, 36) (dual of [624, 556, 37]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,35], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(2572, 624, F25, 38) (dual of [624, 552, 39]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−2,−1,…,35}, and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(2566, 624, F25, 35) (dual of [624, 558, 36]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,34], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(251, 5, F25, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(251, 25, F25, 1) (dual of [25, 24, 2]-code), using
- Reed–Solomon code RS(24,25) [i]
- discarding factors / shortening the dual code based on linear OA(251, 25, F25, 1) (dual of [25, 24, 2]-code), using
- linear OA(250, 2, F25, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(250, s, F25, 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 OA(5147, 1263, F5, 38) (dual of [1263, 1116, 39]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(5146, 631, F5, 2, 38) (dual of [(631, 2), 1116, 39]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(5146, 420, F5, 3, 38) (dual of [(420, 3), 1114, 39]-NRT-code) | [i] | ||