Information on Result #677687

Linear OA(3137, 151, F3, 77) (dual of [151, 14, 78]-code), using construction XX applied to C1 = C([0,60]), C2 = C([1,75]), C3 = C1 + C2 = C([1,60]), and C∩ = C1 ∩ C2 = C([0,75]) based on
  1. linear OA(3106, 121, F3, 62) (dual of [121, 15, 63]-code), using the expurgated narrow-sense BCH-code C(I) with length 121 | 35−1, defining interval I = [0,60], and minimum distance d ≥ |{−1,0,…,60}|+1 = 63 (BCH-bound) [i]
  2. linear OA(3115, 121, F3, 75) (dual of [121, 6, 76]-code), using the narrow-sense BCH-code C(I) with length 121 | 35−1, defining interval I = [1,75], and designed minimum distance d ≥ |I|+1 = 76 [i]
  3. linear OA(3116, 121, F3, 80) (dual of [121, 5, 81]-code), using the expurgated narrow-sense BCH-code C(I) with length 121 | 35−1, defining interval I = [0,75], and minimum distance d ≥ |{5,15,25,…,−52}|+1 = 81 (BCH-bound) [i]
  4. linear OA(3105, 121, F3, 60) (dual of [121, 16, 61]-code), using the narrow-sense BCH-code C(I) with length 121 | 35−1, defining interval I = [1,60], and designed minimum distance d ≥ |I|+1 = 61 [i]
  5. linear OA(31, 2, F3, 1) (dual of [2, 1, 2]-code), using
  6. 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(3135, 149, F3, 75) (dual of [149, 14, 76]-code) [i]Truncation
2Linear OOA(3137, 75, F3, 2, 77) (dual of [(75, 2), 13, 78]-NRT-code) [i]OOA Folding
3Linear OOA(3137, 50, F3, 3, 77) (dual of [(50, 3), 13, 78]-NRT-code) [i]
4Linear OOA(3137, 30, F3, 5, 77) (dual of [(30, 5), 13, 78]-NRT-code) [i]