Information on Result #2267645
Linear OA(3244, 771, F3, 61) (dual of [771, 527, 62]-code), using 2 times code embedding in larger space based on linear OA(3242, 769, F3, 61) (dual of [769, 527, 62]-code), using
- construction XX applied to C1 = C([307,363]), C2 = C([313,367]), C3 = C1 + C2 = C([313,363]), and C∩ = C1 ∩ C2 = C([307,367]) [i] based on
- linear OA(3216, 728, F3, 57) (dual of [728, 512, 58]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {307,308,…,363}, and designed minimum distance d ≥ |I|+1 = 58 [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(3201, 728, F3, 51) (dual of [728, 527, 52]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {313,314,…,363}, and designed minimum distance d ≥ |I|+1 = 52 [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(35, 18, F3, 3) (dual of [18, 13, 4]-code or 18-cap in PG(4,3)), 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(3244, 257, F3, 3, 61) (dual of [(257, 3), 527, 62]-NRT-code) | [i] | OOA Folding | |