MinT - Information on Result #976838

Information on Result #976838

Linear OOA(7³⁰, 12, F₇, 3, 23) (dual of [(12, 3), 6, 24]-NRT-code), using OOA 3-folding based on linear OA(7³⁰, 36, F₇, 23) (dual of [36, 6, 24]-code), using

generalized (u,Â u+v)-construction [i] based on
1. 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
  - discarding factors / shortening the dual code based on linear OA(7³, 7, F₇, 3) (dual of [7, 4, 4]-code or 7-arc in PG(2,7) or 7-cap in PG(2,7)), using
    - Reedâ€“Solomon code RS(4,7) [i]
2. linear OA(7⁴, 6, F₇, 4) (dual of [6, 2, 5]-code or 6-arc in PG(3,7)), using
  - discarding factors / shortening the dual code based on linear OA(7⁴, 7, F₇, 4) (dual of [7, 3, 5]-code or 7-arc in PG(3,7)), using
    - Reedâ€“Solomon code RS(3,7) [i]
3. linear OA(7⁵, 6, F₇, 5) (dual of [6, 1, 6]-code or 6-arc in PG(4,7)), using
  - dual of repetition code with length 6 [i]
4. linear OA(7⁶, 6, F₇, 6) (dual of [6, 0, 7]-code or 6-arc in PG(5,7)), using
  - complete OA / dual of code with only one code word [i]
5. linear OA(7⁶, 6, F₇, 6) (dual of [6, 0, 7]-code or 6-arc in PG(5,7)) (see above)
6. linear OA(7⁶, 6, F₇, 6) (dual of [6, 0, 7]-code or 6-arc in PG(5,7)) (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.