Information on Result #705709
Linear OA(3238, 770, F3, 59) (dual of [770, 532, 60]-code), using construction XX applied to C1 = C([307,364]), C2 = C([315,365]), C3 = C1 + C2 = C([315,364]), and C∩ = C1 ∩ C2 = C([307,365]) based on
- linear OA(3217, 728, F3, 58) (dual of [728, 511, 59]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {307,308,…,364}, and designed minimum distance d ≥ |I|+1 = 59 [i]
- linear OA(3202, 728, F3, 51) (dual of [728, 526, 52]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {315,316,…,365}, and designed minimum distance d ≥ |I|+1 = 52 [i]
- linear OA(3223, 728, F3, 59) (dual of [728, 505, 60]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {307,308,…,365}, and designed minimum distance d ≥ |I|+1 = 60 [i]
- linear OA(3196, 728, F3, 50) (dual of [728, 532, 51]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {315,316,…,364}, and designed minimum distance d ≥ |I|+1 = 51 [i]
- linear OA(315, 36, F3, 7) (dual of [36, 21, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(315, 41, F3, 7) (dual of [41, 26, 8]-code), using
- an extension Ce(6) of the narrow-sense BCH-code C(I) with length 40 | 34−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- discarding factors / shortening the dual code based on linear OA(315, 41, F3, 7) (dual of [41, 26, 8]-code), 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 OOA(3238, 385, F3, 2, 59) (dual of [(385, 2), 532, 60]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(3238, 256, F3, 3, 59) (dual of [(256, 3), 530, 60]-NRT-code) | [i] | ||
| 3 | Linear OOA(3238, 192, F3, 4, 59) (dual of [(192, 4), 530, 60]-NRT-code) | [i] | ||