Information on Result #711308
Linear OA(578, 649, F5, 23) (dual of [649, 571, 24]-code), using construction XX applied to C1 = C([141,161]), C2 = C([139,157]), C3 = C1 + C2 = C([141,157]), and C∩ = C1 ∩ C2 = C([139,161]) based on
- linear OA(565, 624, F5, 21) (dual of [624, 559, 22]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {141,142,…,161}, and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(561, 624, F5, 19) (dual of [624, 563, 20]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {139,140,…,157}, and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(573, 624, F5, 23) (dual of [624, 551, 24]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {139,140,…,161}, and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(553, 624, F5, 17) (dual of [624, 571, 18]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {141,142,…,157}, and designed minimum distance d ≥ |I|+1 = 18 [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(579, 650, F5, 23) (dual of [650, 571, 24]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(578, 324, F5, 2, 23) (dual of [(324, 2), 570, 24]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(578, 216, F5, 3, 23) (dual of [(216, 3), 570, 24]-NRT-code) | [i] | ||