Information on Result #705381
Linear OA(3196, 758, F3, 48) (dual of [758, 562, 49]-code), using construction XX applied to C1 = C([724,42]), C2 = C([0,43]), C3 = C1 + C2 = C([0,42]), and C∩ = C1 ∩ C2 = C([724,43]) based on
- linear OA(3184, 728, F3, 47) (dual of [728, 544, 48]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−4,−3,…,42}, and designed minimum distance d ≥ |I|+1 = 48 [i]
- linear OA(3172, 728, F3, 44) (dual of [728, 556, 45]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,43], and designed minimum distance d ≥ |I|+1 = 45 [i]
- linear OA(3190, 728, F3, 48) (dual of [728, 538, 49]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−4,−3,…,43}, and designed minimum distance d ≥ |I|+1 = 49 [i]
- linear OA(3166, 728, F3, 43) (dual of [728, 562, 44]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,42], and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(36, 24, F3, 3) (dual of [24, 18, 4]-code or 24-cap in PG(5,3)), using
- discarding factors / shortening the dual code based on linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), 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 OOA(3196, 379, F3, 2, 48) (dual of [(379, 2), 562, 49]-NRT-code) | [i] | OOA Folding | |