Information on Result #705248
Linear OA(3186, 766, F3, 45) (dual of [766, 580, 46]-code), using construction XX applied to C1 = C([328,370]), C2 = C([325,365]), C3 = C1 + C2 = C([328,365]), and C∩ = C1 ∩ C2 = C([325,370]) based on
- linear OA(3166, 728, F3, 43) (dual of [728, 562, 44]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {328,329,…,370}, and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(3160, 728, F3, 41) (dual of [728, 568, 42]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {325,326,…,365}, and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(3178, 728, F3, 46) (dual of [728, 550, 47]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {325,326,…,370}, and designed minimum distance d ≥ |I|+1 = 47 [i]
- linear OA(3148, 728, F3, 38) (dual of [728, 580, 39]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {328,329,…,365}, and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(37, 25, F3, 4) (dual of [25, 18, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(37, 26, F3, 4) (dual of [26, 19, 5]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 26 = 33−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(37, 26, F3, 4) (dual of [26, 19, 5]-code), using
- linear OA(31, 13, F3, 1) (dual of [13, 12, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-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(3186, 383, F3, 2, 45) (dual of [(383, 2), 580, 46]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(3186, 255, F3, 3, 45) (dual of [(255, 3), 579, 46]-NRT-code) | [i] | ||