MinT - Information on Result #641433

Information on Result #641433

Linear OA(8¹³⁹, 144, F₈, 112) (dual of [144, 5, 113]-code), using juxtaposition based on

linear OA(8⁵⁷, 62, F₈, 48) (dual of [62, 5, 49]-code), using
- 3 times truncation [i] based on linear OA(8⁶⁰, 65, F₈, 51) (dual of [65, 5, 52]-code), using
  - constructionÂ X applied to AG(F,12P) âŠ‚ AG(F,13P) [i] based on
    1. linear OA(8⁶⁰, 64, F₈, 51) (dual of [64, 4, 52]-code), using algebraic-geometric code AG(F,12P) with known gap numbers [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using the Suzuki function field over F₈ [i]
    2. linear OA(8⁵⁹, 64, F₈, 50) (dual of [64, 5, 51]-code), using algebraic-geometric code AG(F,13P) with known gap numbers [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
    3. linear OA(8⁰, 1, F₈, 0) (dual of [1, 1, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(8⁰, s, F₈, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]
linear OA(8⁷⁷, 82, F₈, 63) (dual of [82, 5, 64]-code), using
- discarding factors / shortening the dual code based on linear OA(8⁷⁷, 83, F₈, 63) (dual of [83, 6, 64]-code), using
  - constructionÂ X applied to C₁ âŠ‚ C₀ [i] based on
    1. linear OA(8⁷⁰, 73, F₈, 63) (dual of [73, 3, 64]-code), using code C₁ for uÂ =Â 3 by de Boer and Brouwer [i]
    2. linear OA(8⁶⁷, 73, F₈, 55) (dual of [73, 6, 56]-code), using code C₀ for uÂ =Â 3 by de Boer and Brouwer [i]
    3. linear OA(8⁷, 10, F₈, 7) (dual of [10, 3, 8]-code or 10-arc in PG(6,8)), using
      - Denniston code D(1,8) [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

None.