MinT - Information on Result #875609

Information on Result #875609

Linear OOA(64⁷⁹, 258, F₆₄, 2, 49) (dual of [(258, 2), 437, 50]-NRT-code), using OOA 2-folding based on linear OA(64⁷⁹, 516, F₆₄, 49) (dual of [516, 437, 50]-code), using

discarding factors / shortening the dual code based on linear OA(64⁷⁹, 517, F₆₄, 49) (dual of [517, 438, 50]-code), using
- constructionÂ X applied to AG(F,462P) âŠ‚ AG(F,465P) [i] based on
  1. linear OA(64⁷⁷, 512, F₆₄, 49) (dual of [512, 435, 50]-code), using algebraic-geometric code AG(F,462P) [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
    - the Hermitian function field over F₆₄ [i]
  2. linear OA(64⁷⁴, 512, F₆₄, 46) (dual of [512, 438, 47]-code), using algebraic-geometric code AG(F,465P) [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513 (see above)
  3. linear OA(64², 5, F₆₄, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,64)), using
    - discarding factors / shortening the dual code based on linear OA(64², 64, F₆₄, 2) (dual of [64, 62, 3]-code or 64-arc in PG(1,64)), using
      - Reedâ€“Solomon code RS(62,64) [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.