MinT - Information on Result #844442

Information on Result #844442

Linear OOA(8³⁰, 18, F₈, 2, 23) (dual of [(18, 2), 6, 24]-NRT-code), using OOA 2-folding based on linear OA(8³⁰, 36, F₈, 23) (dual of [36, 6, 24]-code), using

generalized (u,Â u+v)-construction [i] based on
1. linear OA(8³, 6, F₈, 3) (dual of [6, 3, 4]-code or 6-arc in PG(2,8) or 6-cap in PG(2,8)), using
  - discarding factors / shortening the dual code based on linear OA(8³, 8, F₈, 3) (dual of [8, 5, 4]-code or 8-arc in PG(2,8) or 8-cap in PG(2,8)), using
    - Reedâ€“Solomon code RS(5,8) [i]
2. linear OA(8⁴, 6, F₈, 4) (dual of [6, 2, 5]-code or 6-arc in PG(3,8)), using
  - discarding factors / shortening the dual code based on linear OA(8⁴, 8, F₈, 4) (dual of [8, 4, 5]-code or 8-arc in PG(3,8)), using
    - Reedâ€“Solomon code RS(4,8) [i]
3. linear OA(8⁵, 6, F₈, 5) (dual of [6, 1, 6]-code or 6-arc in PG(4,8)), using
  - dual of repetition code with length 6 [i]
4. linear OA(8⁶, 6, F₈, 6) (dual of [6, 0, 7]-code or 6-arc in PG(5,8)), using
  - complete OA / dual of code with only one code word [i]
5. linear OA(8⁶, 6, F₈, 6) (dual of [6, 0, 7]-code or 6-arc in PG(5,8)) (see above)
6. linear OA(8⁶, 6, F₈, 6) (dual of [6, 0, 7]-code or 6-arc in PG(5,8)) (see above)

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

None.