MinT - Information on Result #2499543

Information on Result #2499543

Linear OOA(4²²⁴, 556, F₄, 2, 58) (dual of [(556, 2), 888, 59]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(4²²², 555, F₄, 2, 58) (dual of [(555, 2), 888, 59]-NRT-code), using

trace code [i] based on linear OOA(64⁷⁴, 185, F₆₄, 2, 58) (dual of [(185, 2), 296, 59]-NRT-code), using
- constructionÂ X applied to AG(2;F,293P) âŠ‚ AG(2;F,303P) [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(64⁵⁵, 176, F₆₄, 2, 48) (dual of [(176, 2), 297, 49]-NRT-code), using algebraic-geometric NRT-code AG(2;F,303P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177 (see above)
  3. linear OOA(64⁹, 9, F₆₄, 2, 9) (dual of [(9, 2), 9, 10]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(64⁹, 64, F₆₄, 2, 9) (dual of [(64, 2), 119, 10]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;119,64) [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.