Information on Result #641456

Linear OA(8134, 138, F8, 116) (dual of [138, 4, 117]-code), using juxtaposition based on
  1. linear OA(84, 8, F8, 4) (dual of [8, 4, 5]-code or 8-arc in PG(3,8)), using
  2. linear OA(8126, 130, F8, 111) (dual of [130, 4, 112]-code), using
    • repeating each code word 2 times [i] based on linear OA(861, 65, F8, 55) (dual of [65, 4, 56]-code), using
      • projective code from ovoid in PG(3, 8) [i]
      • the expurgated narrow-sense BCH-code C(I) with length 65 | 84−1, defining interval I = [0,27], and minimum distance d ≥ |{−27,−26,…,27}|+1 = 56 (BCH-bound) [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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OA(8134, 138, F8, 115) (dual of [138, 4, 116]-code) [i]Strength Reduction
2Linear OA(8134, 138, F8, 114) (dual of [138, 4, 115]-code) [i]
3Linear OA(8134, 138, F8, 113) (dual of [138, 4, 114]-code) [i]
4Linear OA(8134, 138, F8, 112) (dual of [138, 4, 113]-code) [i]
5Linear OA(8142, 146, F8, 121) (dual of [146, 4, 122]-code) [i]Juxtaposition
6Linear OA(8143, 147, F8, 122) (dual of [147, 4, 123]-code) [i]
7Linear OOA(8134, 69, F8, 2, 116) (dual of [(69, 2), 4, 117]-NRT-code) [i]OOA Folding
8Linear OOA(8134, 46, F8, 3, 116) (dual of [(46, 3), 4, 117]-NRT-code) [i]