Information on Result #685808

Linear OA(795, 104, F7, 69) (dual of [104, 9, 70]-code), using construction XX applied to C1 = C([0,63]), C2 = C([1,67]), C3 = C1 + C2 = C([1,63]), and C∩ = C1 ∩ C2 = C([0,67]) based on
  1. 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]
  2. linear OA(790, 96, F7, 67) (dual of [96, 6, 68]-code), using the narrow-sense BCH-code C(I) with length 96 | 74−1, defining interval I = [1,67], and designed minimum distance d ≥ |I|+1 = 68 [i]
  3. linear OA(791, 96, F7, 69) (dual of [96, 5, 70]-code), using the expurgated narrow-sense BCH-code C(I) with length 96 | 74−1, defining interval I = [0,67], and minimum distance d ≥ |{−1,0,…,67}|+1 = 70 (BCH-bound) [i]
  4. 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]
  5. linear OA(71, 2, F7, 1) (dual of [2, 1, 2]-code), using
  6. linear OA(73, 6, F7, 3) (dual of [6, 3, 4]-code or 6-arc in PG(2,7) or 6-cap in PG(2,7)), 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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OA(795, 104, F7, 68) (dual of [104, 9, 69]-code) [i]Strength Reduction
2Linear OA(793, 102, F7, 67) (dual of [102, 9, 68]-code) [i]Truncation
3Linear OA(792, 101, F7, 66) (dual of [101, 9, 67]-code) [i]
4Linear OA(790, 99, F7, 64) (dual of [99, 9, 65]-code) [i]
5Linear OA(788, 97, F7, 62) (dual of [97, 9, 63]-code) [i]
6Linear OA(786, 95, F7, 60) (dual of [95, 9, 61]-code) [i]
7Linear OOA(795, 52, F7, 2, 69) (dual of [(52, 2), 9, 70]-NRT-code) [i]OOA Folding