MinT - Information on Result #875615

Information on Result #875615

Linear OOA(64⁸⁵, 264, F₆₄, 2, 49) (dual of [(264, 2), 443, 50]-NRT-code), using OOA 2-folding based on linear OA(64⁸⁵, 528, F₆₄, 49) (dual of [528, 443, 50]-code), using

discarding factors / shortening the dual code based on linear OA(64⁸⁵, 529, F₆₄, 49) (dual of [529, 444, 50]-code), using
- constructionÂ X applied to AG(F,462P) âŠ‚ AG(F,471P) [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(64⁶⁸, 512, F₆₄, 40) (dual of [512, 444, 41]-code), using algebraic-geometric code AG(F,471P) [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513 (see above)
  3. linear OA(64⁸, 17, F₆₄, 8) (dual of [17, 9, 9]-code or 17-arc in PG(7,64)), using
    - discarding factors / shortening the dual code based on linear OA(64⁸, 64, F₆₄, 8) (dual of [64, 56, 9]-code or 64-arc in PG(7,64)), using
      - Reedâ€“Solomon code RS(56,64) [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.