Information on Result #738322

Linear OA(8168, 172, F8, 145) (dual of [172, 4, 146]-code), using juxtaposition based on
  1. linear OA(838, 42, F8, 33) (dual of [42, 4, 34]-code), 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(8168, 172, F8, 144) (dual of [172, 4, 145]-code) [i]Strength Reduction
2Linear OA(8168, 172, F8, 143) (dual of [172, 4, 144]-code) [i]
3Linear OA(8168, 172, F8, 142) (dual of [172, 4, 143]-code) [i]
4Linear OA(8168, 172, F8, 141) (dual of [172, 4, 142]-code) [i]
5Linear OA(8168, 172, F8, 140) (dual of [172, 4, 141]-code) [i]
6Linear OA(8168, 172, F8, 139) (dual of [172, 4, 140]-code) [i]
7Linear OOA(8168, 86, F8, 2, 145) (dual of [(86, 2), 4, 146]-NRT-code) [i]OOA Folding