Information on Result #704574
Linear OA(3123, 754, F3, 30) (dual of [754, 631, 31]-code), using construction XX applied to C1 = C([336,364]), C2 = C([340,365]), C3 = C1 + C2 = C([340,364]), and C∩ = C1 ∩ C2 = C([336,365]) based on
- linear OA(3112, 728, F3, 29) (dual of [728, 616, 30]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {336,337,…,364}, and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(3103, 728, F3, 26) (dual of [728, 625, 27]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {340,341,…,365}, and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(3118, 728, F3, 30) (dual of [728, 610, 31]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {336,337,…,365}, and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(397, 728, F3, 25) (dual of [728, 631, 26]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {340,341,…,364}, and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(35, 20, F3, 3) (dual of [20, 15, 4]-code or 20-cap in PG(4,3)), using
- linear OA(30, 6, F3, 0) (dual of [6, 6, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 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(3125, 758, F3, 30) (dual of [758, 633, 31]-code) | [i] | Varšamov–Edel Lengthening | |
| 2 | Linear OOA(3123, 377, F3, 2, 30) (dual of [(377, 2), 631, 31]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(3123, 251, F3, 3, 30) (dual of [(251, 3), 630, 31]-NRT-code) | [i] | ||
| 4 | Linear OOA(3123, 188, F3, 4, 30) (dual of [(188, 4), 629, 31]-NRT-code) | [i] | ||