MinT - Information on Result #846555

Information on Result #846555

Linear OOA(8¹¹⁴, 189, F₈, 2, 44) (dual of [(189, 2), 264, 45]-NRT-code), using OOA 2-folding based on linear OA(8¹¹⁴, 378, F₈, 44) (dual of [378, 264, 45]-code), using

trace code [i] based on linear OA(64⁵⁷, 189, F₆₄, 44) (dual of [189, 132, 45]-code), using
- constructionÂ X applied to AG(F,131P) âŠ‚ AG(F,138P) [i] based on
  1. 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, using
    - a function field by GarcÃa and Quoos [i]
  2. linear OA(64⁴⁴, 176, F₆₄, 37) (dual of [176, 132, 38]-code), using algebraic-geometric code AG(F,138P) [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.