MinT - Information on Result #828296

Information on Result #828296

Linear OOA(4¹⁹⁵, 274, F₄, 2, 55) (dual of [(274, 2), 353, 56]-NRT-code), using OOA 2-folding based on linear OA(4¹⁹⁵, 548, F₄, 55) (dual of [548, 353, 56]-code), using

discarding factors / shortening the dual code based on linear OA(4¹⁹⁵, 549, F₄, 55) (dual of [549, 354, 56]-code), using
- trace code [i] based on linear OA(64⁶⁵, 183, F₆₄, 55) (dual of [183, 118, 56]-code), using
  - constructionÂ X applied to AG(F,120P) âŠ‚ AG(F,124P) [i] based on
    1. linear OA(64⁶², 176, F₆₄, 55) (dual of [176, 114, 56]-code), using algebraic-geometric code AG(F,120P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]
    2. linear OA(64⁵⁸, 176, F₆₄, 51) (dual of [176, 118, 52]-code), using algebraic-geometric code AG(F,124P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177 (see above)
    3. linear OA(64³, 7, F₆₄, 3) (dual of [7, 4, 4]-code or 7-arc in PG(2,64) or 7-cap in PG(2,64)), using
      - discarding factors / shortening the dual code based on linear OA(64³, 64, F₆₄, 3) (dual of [64, 61, 4]-code or 64-arc in PG(2,64) or 64-cap in PG(2,64)), using
        Reedâ€“Solomon code RS(61,64) [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.