MinT - Information on Result #875742

Information on Result #875742

Linear OOA(64⁷⁸, 106, F₆₄, 2, 53) (dual of [(106, 2), 134, 54]-NRT-code), using OOA 2-folding based on linear OA(64⁷⁸, 212, F₆₄, 53) (dual of [212, 134, 54]-code), using

discarding factors / shortening the dual code based on linear OA(64⁷⁸, 213, F₆₄, 53) (dual of [213, 135, 54]-code), using
- constructionÂ X applied to AG(F,122P) âŠ‚ AG(F,141P) [i] based on
  1. linear OA(64⁶⁰, 176, F₆₄, 53) (dual of [176, 116, 54]-code), using algebraic-geometric code AG(F,122P) [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(64⁴¹, 176, F₆₄, 34) (dual of [176, 135, 35]-code), using algebraic-geometric code AG(F,141P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177 (see above)
  3. linear OA(64¹⁸, 37, F₆₄, 18) (dual of [37, 19, 19]-code or 37-arc in PG(17,64)), using
    - discarding factors / shortening the dual code based on linear OA(64¹⁸, 64, F₆₄, 18) (dual of [64, 46, 19]-code or 64-arc in PG(17,64)), using
      - Reedâ€“Solomon code RS(46,64) [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.