MinT - Information on Result #2282211

Information on Result #2282211

Linear OA(8¹²⁹, 367, F₈, 54) (dual of [367, 238, 55]-code), using 1 times code embedding in larger space based on linear OA(8¹²⁸, 366, F₈, 54) (dual of [366, 238, 55]-code), using

trace code [i] based on linear OA(64⁶⁴, 183, F₆₄, 54) (dual of [183, 119, 55]-code), using
- constructionÂ X applied to AG(F,121P) âŠ‚ AG(F,125P) [i] based on
  1. 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, using
    - a function field by GarcÃa and Quoos [i]
  2. linear OA(64⁵⁷, 176, F₆₄, 50) (dual of [176, 119, 51]-code), using algebraic-geometric code AG(F,125P) [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.