Information on Result #674588

Linear OA(3153, 531482, F3, 19) (dual of [531482, 531329, 20]-code), using construction X applied to Ce(18) ⊂ Ce(13) based on
  1. linear OA(3145, 531441, F3, 19) (dual of [531441, 531296, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
  2. linear OA(3109, 531441, F3, 14) (dual of [531441, 531332, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [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(3153, 265741, F3, 2, 19) (dual of [(265741, 2), 531329, 20]-NRT-code) [i]OOA Folding
2Linear OOA(3153, 177160, F3, 3, 19) (dual of [(177160, 3), 531327, 20]-NRT-code) [i]
3Linear OOA(3153, 132870, F3, 4, 19) (dual of [(132870, 4), 531327, 20]-NRT-code) [i]
4Linear OOA(3153, 106296, F3, 5, 19) (dual of [(106296, 5), 531327, 20]-NRT-code) [i]
5Linear OOA(3153, 59053, F3, 19, 19) (dual of [(59053, 19), 1121854, 20]-NRT-code) [i]OOA Folding and Stacking with Additional Row