MinT - Information on Result #2499546

Information on Result #2499546

Linear OOA(4²²⁹, 561, F₄, 2, 58) (dual of [(561, 2), 893, 59]-NRT-code), using 4¹ times duplication based on linear OOA(4²²⁸, 561, F₄, 2, 58) (dual of [(561, 2), 894, 59]-NRT-code), using

trace code [i] based on linear OOA(64⁷⁶, 187, F₆₄, 2, 58) (dual of [(187, 2), 298, 59]-NRT-code), using
- constructionÂ X applied to AG(2;F,293P) âŠ‚ AG(2;F,305P) [i] based on
  1. linear OOA(64⁶⁵, 176, F₆₄, 2, 58) (dual of [(176, 2), 287, 59]-NRT-code), using algebraic-geometric NRT-code AG(2;F,293P) [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 OOA(64⁵³, 176, F₆₄, 2, 46) (dual of [(176, 2), 299, 47]-NRT-code), using algebraic-geometric NRT-code AG(2;F,305P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177 (see above)
  3. linear OOA(64¹¹, 11, F₆₄, 2, 11) (dual of [(11, 2), 11, 12]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(64¹¹, 64, F₆₄, 2, 11) (dual of [(64, 2), 117, 12]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;117,64) [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.