MinT - Information on Result #2274835

Information on Result #2274835

Linear OA(4²⁵¹, 557, F₄, 72) (dual of [557, 306, 73]-code), using 2 times code embedding in larger space based on linear OA(4²⁴⁹, 555, F₄, 72) (dual of [555, 306, 73]-code), using

trace code [i] based on linear OA(64⁸³, 185, F₆₄, 72) (dual of [185, 102, 73]-code), using
- constructionÂ X applied to AG(F,103P) âŠ‚ AG(F,108P) [i] based on
  1. linear OA(64⁷⁹, 176, F₆₄, 72) (dual of [176, 97, 73]-code), using algebraic-geometric code AG(F,103P) [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(64⁷⁴, 176, F₆₄, 67) (dual of [176, 102, 68]-code), using algebraic-geometric code AG(F,108P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177 (see above)
  3. linear OA(64⁴, 9, F₆₄, 4) (dual of [9, 5, 5]-code or 9-arc in PG(3,64)), using
    - discarding factors / shortening the dual code based on linear OA(64⁴, 64, F₆₄, 4) (dual of [64, 60, 5]-code or 64-arc in PG(3,64)), using
      - Reedâ€“Solomon code RS(60,64) [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.