MinT - Information on Result #875323

Information on Result #875323

Linear OOA(64⁶⁵, 104, F₆₄, 2, 42) (dual of [(104, 2), 143, 43]-NRT-code), using OOA 2-folding based on linear OA(64⁶⁵, 208, F₆₄, 42) (dual of [208, 143, 43]-code), using

discarding factors / shortening the dual code based on linear OA(64⁶⁵, 209, F₆₄, 42) (dual of [209, 144, 43]-code), using
- constructionÂ X applied to AG(F,133P) âŠ‚ AG(F,150P) [i] based on
  1. linear OA(64⁴⁹, 176, F₆₄, 42) (dual of [176, 127, 43]-code), using algebraic-geometric code AG(F,133P) [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(64³², 176, F₆₄, 25) (dual of [176, 144, 26]-code), using algebraic-geometric code AG(F,150P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177 (see above)
  3. linear OA(64¹⁶, 33, F₆₄, 16) (dual of [33, 17, 17]-code or 33-arc in PG(15,64)), using
    - discarding factors / shortening the dual code based on linear OA(64¹⁶, 64, F₆₄, 16) (dual of [64, 48, 17]-code or 64-arc in PG(15,64)), using
      - Reedâ€“Solomon code RS(48,64) [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.