MinT - Information on Result #2274408

Information on Result #2274408

Linear OA(4²²⁴, 569, F₄, 61) (dual of [569, 345, 62]-code), using 2 times code embedding in larger space based on linear OA(4²²², 567, F₄, 61) (dual of [567, 345, 62]-code), using

trace code [i] based on linear OA(64⁷⁴, 189, F₆₄, 61) (dual of [189, 115, 62]-code), using
- constructionÂ X applied to AG(F,114P) âŠ‚ AG(F,121P) [i] based on
  1. linear OA(64⁶⁸, 176, F₆₄, 61) (dual of [176, 108, 62]-code), using algebraic-geometric code AG(F,114P) [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(64⁶¹, 176, F₆₄, 54) (dual of [176, 115, 55]-code), using algebraic-geometric code AG(F,121P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177 (see above)
  3. linear OA(64⁶, 13, F₆₄, 6) (dual of [13, 7, 7]-code or 13-arc in PG(5,64)), using
    - discarding factors / shortening the dual code based on linear OA(64⁶, 64, F₆₄, 6) (dual of [64, 58, 7]-code or 64-arc in PG(5,64)), using
      - Reedâ€“Solomon code RS(58,64) [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.