Information on Result #690860

Linear OA(978, 100, F9, 52) (dual of [100, 22, 53]-code), using construction XX applied to C1 = C([0,83]), C2 = C([1,103]), C3 = C1 + C2 = C([1,83]), and C∩ = C1 ∩ C2 = C([0,103]) based on
  1. linear OA(959, 80, F9, 42) (dual of [80, 21, 43]-code), using contraction [i] based on linear OA(9139, 160, F9, 85) (dual of [160, 21, 86]-code), using the expurgated narrow-sense BCH-code C(I) with length 160 | 94−1, defining interval I = [0,83], and minimum distance d ≥ |{−1,0,…,83}|+1 = 86 (BCH-bound) [i]
  2. linear OA(967, 80, F9, 51) (dual of [80, 13, 52]-code), using contraction [i] based on linear OA(9147, 160, F9, 103) (dual of [160, 13, 104]-code), using the narrow-sense BCH-code C(I) with length 160 | 94−1, defining interval I = [1,103], and designed minimum distance d ≥ |I|+1 = 104 [i]
  3. linear OA(968, 80, F9, 52) (dual of [80, 12, 53]-code), using contraction [i] based on linear OA(9148, 160, F9, 105) (dual of [160, 12, 106]-code), using the expurgated narrow-sense BCH-code C(I) with length 160 | 94−1, defining interval I = [0,103], and minimum distance d ≥ |{−1,0,…,103}|+1 = 106 (BCH-bound) [i]
  4. linear OA(958, 80, F9, 41) (dual of [80, 22, 42]-code), using contraction [i] based on linear OA(9138, 160, F9, 83) (dual of [160, 22, 84]-code), using the narrow-sense BCH-code C(I) with length 160 | 94−1, defining interval I = [1,83], and designed minimum distance d ≥ |I|+1 = 84 [i]
  5. linear OA(90, 1, F9, 0) (dual of [1, 1, 1]-code), using
  6. linear OA(910, 19, F9, 9) (dual of [19, 9, 10]-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 OOA(978, 50, F9, 2, 52) (dual of [(50, 2), 22, 53]-NRT-code) [i]OOA Folding