Information on Result #711078
Linear OA(562, 649, F5, 18) (dual of [649, 587, 19]-code), using construction XX applied to C1 = C([146,161]), C2 = C([144,157]), C3 = C1 + C2 = C([146,157]), and C∩ = C1 ∩ C2 = C([144,161]) based on
- linear OA(549, 624, F5, 16) (dual of [624, 575, 17]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {146,147,…,161}, and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(545, 624, F5, 14) (dual of [624, 579, 15]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {144,145,…,157}, and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(557, 624, F5, 18) (dual of [624, 567, 19]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {144,145,…,161}, and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(537, 624, F5, 12) (dual of [624, 587, 13]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {146,147,…,157}, and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(54, 16, F5, 3) (dual of [16, 12, 4]-code or 16-cap in PG(3,5)), using
- linear OA(51, 9, F5, 1) (dual of [9, 8, 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(563, 650, F5, 18) (dual of [650, 587, 19]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(562, 324, F5, 2, 18) (dual of [(324, 2), 586, 19]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(562, 216, F5, 3, 18) (dual of [(216, 3), 586, 19]-NRT-code) | [i] | ||