Information on Result #677732

Linear OA(385, 109, F3, 40) (dual of [109, 24, 41]-code), using construction X applied to Ce(39) ⊂ Ce(24) based on
  1. linear OA(365, 81, F3, 40) (dual of [81, 16, 41]-code), using an extension Ce(39) of the primitive narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [1,39], and designed minimum distance d ≥ |I|+1 = 40 [i]
  2. linear OA(357, 81, F3, 25) (dual of [81, 24, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
  3. linear OA(320, 28, F3, 14) (dual of [28, 8, 15]-code), using
    • contraction [i] based on linear OA(348, 56, F3, 29) (dual of [56, 8, 30]-code), using the BCH-code C(I) with length 56 | 36−1, defining interval I = {0,1,…,28}, and designed minimum distance d ≥ |I|+1 = 30 [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.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OA(386, 110, F3, 40) (dual of [110, 24, 41]-code) [i]Code Embedding in Larger Space
2Linear OA(389, 113, F3, 40) (dual of [113, 24, 41]-code) [i]
3Linear OA(383, 107, F3, 38) (dual of [107, 24, 39]-code) [i]Truncation
4Linear OA(387, 112, F3, 40) (dual of [112, 25, 41]-code) [i]Construction X with VarÅ¡amov Bound
5Linear OA(389, 115, F3, 40) (dual of [115, 26, 41]-code) [i]
6Linear OOA(385, 54, F3, 2, 40) (dual of [(54, 2), 23, 41]-NRT-code) [i]OOA Folding
7Linear OOA(385, 36, F3, 3, 40) (dual of [(36, 3), 23, 41]-NRT-code) [i]