Information on Result #705620
Linear OA(3223, 769, F3, 54) (dual of [769, 546, 55]-code), using construction XX applied to C1 = C([722,45]), C2 = C([0,48]), C3 = C1 + C2 = C([0,45]), and C∩ = C1 ∩ C2 = C([722,48]) based on
- 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 = {−6,−5,…,45}, and designed minimum distance d ≥ |I|+1 = 53 [i]
- linear OA(3190, 728, F3, 49) (dual of [728, 538, 50]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,48], and designed minimum distance d ≥ |I|+1 = 50 [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 = {−6,−5,…,48}, and designed minimum distance d ≥ |I|+1 = 56 [i]
- linear OA(3178, 728, F3, 46) (dual of [728, 550, 47]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,45], and designed minimum distance d ≥ |I|+1 = 47 [i]
- linear OA(38, 28, F3, 5) (dual of [28, 20, 6]-code), using
- dual code (with bound on d by construction Y1) [i] based on
- 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(3223, 384, F3, 2, 54) (dual of [(384, 2), 545, 55]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(3223, 256, F3, 3, 54) (dual of [(256, 3), 545, 55]-NRT-code) | [i] | ||