Information on Result #677625

Linear OA(389, 105, F3, 50) (dual of [105, 16, 51]-code), using construction XX applied to C([0,99]) ⊂ C([0,81]) ⊂ C([1,79]) based on
  1. linear OA(374, 80, F3, 50) (dual of [80, 6, 51]-code), using contraction [i] based on linear OA(3154, 160, F3, 101) (dual of [160, 6, 102]-code), using the expurgated narrow-sense BCH-code C(I) with length 160 | 38−1, defining interval I = [0,99], and minimum distance d ≥ |{−1,0,…,99}|+1 = 102 (BCH-bound) [i]
  2. linear OA(366, 80, F3, 41) (dual of [80, 14, 42]-code), using contraction [i] based on linear OA(3146, 160, F3, 83) (dual of [160, 14, 84]-code), using the expurgated narrow-sense BCH-code C(I) with length 160 | 38−1, defining interval I = [0,81], and minimum distance d ≥ |{−1,0,…,81}|+1 = 84 (BCH-bound) [i]
  3. linear OA(364, 80, F3, 39) (dual of [80, 16, 40]-code), using contraction [i] based on linear OA(3144, 160, F3, 79) (dual of [160, 16, 80]-code), using the narrow-sense BCH-code C(I) with length 160 | 38−1, defining interval I = [1,79], and designed minimum distance d ≥ |I|+1 = 80 [i]
  4. linear OA(312, 22, F3, 8) (dual of [22, 10, 9]-code), using
  5. linear OA(31, 3, F3, 1) (dual of [3, 2, 2]-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.

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(389, 105, F3, 49) (dual of [105, 16, 50]-code) [i]Strength Reduction
2Linear OA(389, 105, F3, 48) (dual of [105, 16, 49]-code) [i]
3Linear OA(389, 105, F3, 47) (dual of [105, 16, 48]-code) [i]
4Linear OA(384, 100, F3, 45) (dual of [100, 16, 46]-code) [i]Truncation
5Linear OOA(389, 35, F3, 3, 50) (dual of [(35, 3), 16, 51]-NRT-code) [i]OOA Folding