Information on Result #675072

Linear OA(3117, 19725, F3, 18) (dual of [19725, 19608, 19]-code), using construction X applied to C([0,9]) ⊂ C([0,6]) based on
  1. 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]
  2. linear OA(373, 19684, F3, 13) (dual of [19684, 19611, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 318−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
  3. linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-code), using
    • the narrow-sense BCH-code C(I) with length 41 | 38−1, defining interval I = [1,1], and minimum distance d ≥ |{−3,−1,1,3}|+1 = 5 (BCH-bound) [i]

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 OOA(3117, 9862, F3, 2, 18) (dual of [(9862, 2), 19607, 19]-NRT-code) [i]OOA Folding
2Linear OOA(3117, 6575, F3, 3, 18) (dual of [(6575, 3), 19608, 19]-NRT-code) [i]
3Linear OOA(3117, 4931, F3, 4, 18) (dual of [(4931, 4), 19607, 19]-NRT-code) [i]
4Linear OOA(3117, 3945, F3, 5, 18) (dual of [(3945, 5), 19608, 19]-NRT-code) [i]
5Linear OOA(3117, 2191, F3, 18, 18) (dual of [(2191, 18), 39321, 19]-NRT-code) [i]OA Folding and Stacking