MinT - Information on Result #875720

Information on Result #875720

Linear OOA(64⁸⁸, 264, F₆₄, 2, 52) (dual of [(264, 2), 440, 53]-NRT-code), using OOA 2-folding based on linear OA(64⁸⁸, 528, F₆₄, 52) (dual of [528, 440, 53]-code), using

discarding factors / shortening the dual code based on linear OA(64⁸⁸, 529, F₆₄, 52) (dual of [529, 441, 53]-code), using
- constructionÂ X applied to AG(F,459P) âŠ‚ AG(F,468P) [i] based on
  1. linear OA(64⁸⁰, 512, F₆₄, 52) (dual of [512, 432, 53]-code), using algebraic-geometric code AG(F,459P) [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(64⁷¹, 512, F₆₄, 43) (dual of [512, 441, 44]-code), using algebraic-geometric code AG(F,468P) [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.