MinT - Information on Result #2499259

Information on Result #2499259

Linear OOA(4²¹⁴, 555, F₄, 2, 55) (dual of [(555, 2), 896, 56]-NRT-code), using 4¹ times duplication based on linear OOA(4²¹³, 555, F₄, 2, 55) (dual of [(555, 2), 897, 56]-NRT-code), using

trace code [i] based on linear OOA(64⁷¹, 185, F₆₄, 2, 55) (dual of [(185, 2), 299, 56]-NRT-code), using
- constructionÂ X applied to AG(2;F,296P) âŠ‚ AG(2;F,306P) [i] based on
  1. linear OOA(64⁶², 176, F₆₄, 2, 55) (dual of [(176, 2), 290, 56]-NRT-code), using algebraic-geometric NRT-code AG(2;F,296P) [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(64⁵², 176, F₆₄, 2, 45) (dual of [(176, 2), 300, 46]-NRT-code), using algebraic-geometric NRT-code AG(2;F,306P) [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.