MinT - Information on Result #626062

Information on Result #626062

Linear OA(8¹³⁹, 144, F₈, 104) (dual of [144, 5, 105]-code), using repeating each code word 3 times based on linear OA(8⁴³, 48, F₈, 34) (dual of [48, 5, 35]-code), using

discarding factors / shortening the dual code based on linear OA(8⁴³, 49, F₈, 34) (dual of [49, 6, 35]-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OA(8⁴, 7, F₈, 4) (dual of [7, 3, 5]-code or 7-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]
  2. linear OA(8⁵, 7, F₈, 5) (dual of [7, 2, 6]-code or 7-arc in PG(4,8)), using
    - discarding factors / shortening the dual code based on linear OA(8⁵, 8, F₈, 5) (dual of [8, 3, 6]-code or 8-arc in PG(4,8)), using
      - Reedâ€“Solomon code RS(3,8) [i]
  3. linear OA(8⁶, 7, F₈, 6) (dual of [7, 1, 7]-code or 7-arc in PG(5,8)), using
    - dual of repetition code with length 7 [i]
  4. linear OA(8⁷, 7, F₈, 7) (dual of [7, 0, 8]-code or 7-arc in PG(6,8)), using
    - complete OA / dual of code with only one code word [i]
  5. linear OA(8⁷, 7, F₈, 7) (dual of [7, 0, 8]-code or 7-arc in PG(6,8)) (see above)
  6. linear OA(8⁷, 7, F₈, 7) (dual of [7, 0, 8]-code or 7-arc in PG(6,8)) (see above)
  7. linear OA(8⁷, 7, F₈, 7) (dual of [7, 0, 8]-code or 7-arc in PG(6,8)) (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.