MinT - Information on Result #2282143

Information on Result #2282143

Linear OA(8¹²⁹, 379, F₈, 51) (dual of [379, 250, 52]-code), using 1 times code embedding in larger space based on linear OA(8¹²⁸, 378, F₈, 51) (dual of [378, 250, 52]-code), using

trace code [i] based on linear OA(64⁶⁴, 189, F₆₄, 51) (dual of [189, 125, 52]-code), using
- constructionÂ X applied to AG(F,124P) âŠ‚ AG(F,131P) [i] based on
  1. 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, using
    - a function field by GarcÃa and Quoos [i]
  2. linear OA(64⁵¹, 176, F₆₄, 44) (dual of [176, 125, 45]-code), using algebraic-geometric code AG(F,131P) [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.