MinT - Information on Result #641261

Information on Result #641261

Linear OA(7⁷⁰, 75, F₇, 53) (dual of [75, 5, 54]-code), using juxtaposition based on

linear OA(7⁵, 10, F₇, 4) (dual of [10, 5, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(7⁵, 11, F₇, 4) (dual of [11, 6, 5]-code), using
  - constructionÂ X applied to AG(F, Q+0P) âŠ‚ AG(F, Q+1P) [i] based on
    1. linear OA(7⁴, 8, F₇, 4) (dual of [8, 4, 5]-code or 8-arc in PG(3,7)), using algebraic-geometric code AG(F, Q+0P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F₇ with g(F) = 0 and N(F) ≥ 8, using the rational function field F₇(x) [i]
    2. linear OA(7², 8, F₇, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,7)), using algebraic-geometric code AG(F, Q+1P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F₇ with g(F) = 0 and N(F) ≥ 8 (see above)
    3. linear OA(7¹, 3, F₇, 1) (dual of [3, 2, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(7¹, s, F₇, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
linear OA(7⁶⁰, 65, F₇, 48) (dual of [65, 5, 49]-code), using
- constructionÂ X applied to C₁ âŠ‚ C₀ [i] based on
  1. linear OA(7⁵⁴, 57, F₇, 48) (dual of [57, 3, 49]-code), using code C₁ for uÂ =Â 3 by de Boer and Brouwer [i]
  2. linear OA(7⁵¹, 57, F₇, 41) (dual of [57, 6, 42]-code), using code C₀ for uÂ =Â 3 by de Boer and Brouwer [i]
  3. linear OA(7⁶, 8, F₇, 6) (dual of [8, 2, 7]-code or 8-arc in PG(5,7)), using
    - extended Reedâ€“Solomon code RS_e(2,7) [i]
    - Simplex code S(2,7) [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.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

None.