Information on Result #835450
Linear OOA(517, 65, F5, 2, 7) (dual of [(65, 2), 113, 8]-NRT-code), using OOA 2-folding based on linear OA(517, 130, F5, 7) (dual of [130, 113, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(517, 131, F5, 7) (dual of [131, 114, 8]-code), using
- construction XX applied to C1 = C([26,31]), C2 = C([28,32]), C3 = C1 + C2 = C([28,31]), and C∩ = C1 ∩ C2 = C([26,32]) [i] based on
- linear OA(513, 124, F5, 6) (dual of [124, 111, 7]-code), using the primitive BCH-code C(I) with length 124 = 53−1, defining interval I = {26,27,…,31}, and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(513, 124, F5, 5) (dual of [124, 111, 6]-code), using the primitive BCH-code C(I) with length 124 = 53−1, defining interval I = {28,29,30,31,32}, and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(516, 124, F5, 7) (dual of [124, 108, 8]-code), using the primitive BCH-code C(I) with length 124 = 53−1, defining interval I = {26,27,…,32}, and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(510, 124, F5, 4) (dual of [124, 114, 5]-code), using the primitive BCH-code C(I) with length 124 = 53−1, defining interval I = {28,29,30,31}, and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(51, 4, F5, 1) (dual of [4, 3, 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, 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 XX applied to C1 = C([26,31]), C2 = C([28,32]), C3 = C1 + C2 = C([28,31]), and C∩ = C1 ∩ C2 = C([26,32]) [i] based on
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(5128, 4194366, F5, 2, 14) (dual of [(4194366, 2), 8388604, 15]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(5137, 4194366, F5, 2, 15) (dual of [(4194366, 2), 8388595, 16]-NRT-code) | [i] | ||