MinT - Information on Result #875610

Information on Result #875610

Linear OOA(64⁸⁰, 259, F₆₄, 2, 49) (dual of [(259, 2), 438, 50]-NRT-code), using OOA 2-folding based on linear OA(64⁸⁰, 518, F₆₄, 49) (dual of [518, 438, 50]-code), using

discarding factors / shortening the dual code based on linear OA(64⁸⁰, 519, F₆₄, 49) (dual of [519, 439, 50]-code), using
- constructionÂ X applied to AG(F,462P) âŠ‚ AG(F,466P) [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(64⁷³, 512, F₆₄, 45) (dual of [512, 439, 46]-code), using algebraic-geometric code AG(F,466P) [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513 (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.