Information on Result #705815
Linear OA(3241, 767, F3, 61) (dual of [767, 526, 62]-code), using construction XX applied to C1 = C([307,364]), C2 = C([313,367]), C3 = C1 + C2 = C([313,364]), and C∩ = C1 ∩ C2 = C([307,367]) 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(3214, 728, F3, 55) (dual of [728, 514, 56]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {313,314,…,367}, and designed minimum distance d ≥ |I|+1 = 56 [i]
- linear OA(3229, 728, F3, 61) (dual of [728, 499, 62]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {307,308,…,367}, and designed minimum distance d ≥ |I|+1 = 62 [i]
- linear OA(3202, 728, F3, 52) (dual of [728, 526, 53]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {313,314,…,364}, and designed minimum distance d ≥ |I|+1 = 53 [i]
- linear OA(38, 23, F3, 5) (dual of [23, 15, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(38, 26, F3, 5) (dual of [26, 18, 6]-code), using
- dual code (with bound on d by construction Y1) [i] based on
- discarding factors / shortening the dual code based on linear OA(38, 26, F3, 5) (dual of [26, 18, 6]-code), using
- linear OA(34, 16, F3, 2) (dual of [16, 12, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- Hamming code H(4,3) [i]
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), 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(3240, 766, F3, 60) (dual of [766, 526, 61]-code) | [i] | Truncation | |
| 2 | Linear OOA(3241, 383, F3, 2, 61) (dual of [(383, 2), 525, 62]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(3241, 255, F3, 3, 61) (dual of [(255, 3), 524, 62]-NRT-code) | [i] | ||
| 4 | Linear OOA(3241, 191, F3, 4, 61) (dual of [(191, 4), 523, 62]-NRT-code) | [i] | ||