Information on Result #685930

Linear OA(755, 66, F7, 36) (dual of [66, 11, 37]-code), using construction XX applied to C1 = C([0,53]), C2 = C([1,79]), C3 = C1 + C2 = C([1,53]), and C∩ = C1 ∩ C2 = C([0,79]) based on
  1. linear OA(738, 48, F7, 27) (dual of [48, 10, 28]-code), using contraction [i] based on linear OA(786, 96, F7, 55) (dual of [96, 10, 56]-code), using the expurgated narrow-sense BCH-code C(I) with length 96 | 74−1, defining interval I = [0,53], and minimum distance d ≥ |{−1,0,…,53}|+1 = 56 (BCH-bound) [i]
  2. linear OA(744, 48, F7, 39) (dual of [48, 4, 40]-code), using contraction [i] based on linear OA(792, 96, F7, 79) (dual of [96, 4, 80]-code), using the narrow-sense BCH-code C(I) with length 96 | 74−1, defining interval I = [1,79], and designed minimum distance d ≥ |I|+1 = 80 [i]
  3. linear OA(745, 48, F7, 40) (dual of [48, 3, 41]-code), using contraction [i] based on linear OA(793, 96, F7, 81) (dual of [96, 3, 82]-code), using the expurgated narrow-sense BCH-code C(I) with length 96 | 74−1, defining interval I = [0,79], and minimum distance d ≥ |{−1,0,…,79}|+1 = 82 (BCH-bound) [i]
  4. linear OA(737, 48, F7, 26) (dual of [48, 11, 27]-code), using contraction [i] based on linear OA(785, 96, F7, 53) (dual of [96, 11, 54]-code), using the narrow-sense BCH-code C(I) with length 96 | 74−1, defining interval I = [1,53], and designed minimum distance d ≥ |I|+1 = 54 [i]
  5. linear OA(70, 1, F7, 0) (dual of [1, 1, 1]-code), using
  6. linear OA(710, 17, F7, 8) (dual of [17, 7, 9]-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

None.