Information on Result #685950

Linear OA(745, 57, F7, 32) (dual of [57, 12, 33]-code), using construction XX applied to C1 = C([0,51]), C2 = C([1,63]), C3 = C1 + C2 = C([1,51]), and C∩ = C1 ∩ C2 = C([0,63]) based on
  1. linear OA(736, 48, F7, 26) (dual of [48, 12, 27]-code), using contraction [i] based on linear OA(784, 96, F7, 53) (dual of [96, 12, 54]-code), using the expurgated narrow-sense BCH-code C(I) with length 96 | 74−1, defining interval I = [0,51], and minimum distance d ≥ |{−1,0,…,51}|+1 = 54 (BCH-bound) [i]
  2. linear OA(739, 48, F7, 31) (dual of [48, 9, 32]-code), using contraction [i] based on linear OA(787, 96, F7, 63) (dual of [96, 9, 64]-code), using the narrow-sense BCH-code C(I) with length 96 | 74−1, defining interval I = [1,63], and designed minimum distance d ≥ |I|+1 = 64 [i]
  3. linear OA(740, 48, F7, 32) (dual of [48, 8, 33]-code), using contraction [i] based on linear OA(788, 96, F7, 65) (dual of [96, 8, 66]-code), using the expurgated narrow-sense BCH-code C(I) with length 96 | 74−1, defining interval I = [0,63], and minimum distance d ≥ |{−1,0,…,63}|+1 = 66 (BCH-bound) [i]
  4. linear OA(735, 48, F7, 25) (dual of [48, 13, 26]-code), using contraction [i] based on linear OA(783, 96, F7, 51) (dual of [96, 13, 52]-code), using the narrow-sense BCH-code C(I) with length 96 | 74−1, defining interval I = [1,51], and designed minimum distance d ≥ |I|+1 = 52 [i]
  5. linear OA(70, 1, F7, 0) (dual of [1, 1, 1]-code), using
  6. linear OA(75, 8, F7, 5) (dual of [8, 3, 6]-code or 8-arc in PG(4,7)), 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(745, 19, F7, 3, 32) (dual of [(19, 3), 12, 33]-NRT-code) [i]OOA Folding