Information on Result #736909

Linear OA(3156, 19731, F3, 25) (dual of [19731, 19575, 26]-code), using construction X applied to C([0,12]) ⊂ C([0,9]) based on
  1. linear OA(3145, 19684, F3, 25) (dual of [19684, 19539, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 318−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
  2. linear OA(3109, 19684, F3, 19) (dual of [19684, 19575, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 318−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
  3. linear OA(311, 47, F3, 5) (dual of [47, 36, 6]-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:

ResultThis
result
only		Method
1Linear OA(3156, 19731, F3, 24) (dual of [19731, 19575, 25]-code) [i]Strength Reduction
2Linear OA(3158, 19733, F3, 25) (dual of [19733, 19575, 26]-code) [i]Code Embedding in Larger Space
3Linear OA(3159, 19734, F3, 25) (dual of [19734, 19575, 26]-code) [i]
4Linear OA(3160, 19735, F3, 25) (dual of [19735, 19575, 26]-code) [i]
5Linear OA(3155, 19730, F3, 24) (dual of [19730, 19575, 25]-code) [i]Truncation
6Linear OA(3160, 19736, F3, 25) (dual of [19736, 19576, 26]-code) [i]Construction X with VarÅ¡amov Bound
7Linear OOA(3156, 9865, F3, 2, 25) (dual of [(9865, 2), 19574, 26]-NRT-code) [i]OOA Folding
8Linear OOA(3156, 6577, F3, 3, 25) (dual of [(6577, 3), 19575, 26]-NRT-code) [i]
9Linear OOA(3156, 4932, F3, 4, 25) (dual of [(4932, 4), 19572, 26]-NRT-code) [i]
10Linear OOA(3156, 3946, F3, 5, 25) (dual of [(3946, 5), 19574, 26]-NRT-code) [i]
11Linear OOA(3156, 1644, F3, 25, 25) (dual of [(1644, 25), 40944, 26]-NRT-code) [i]OOA Folding and Stacking with Additional Row