MinT - Information on Result #2691570

Information on Result #2691570

Linear OOA(4²¹⁵, 540, F₄, 3, 58) (dual of [(540, 3), 1405, 59]-NRT-code), using 4² times duplication based on linear OOA(4²¹³, 540, F₄, 3, 58) (dual of [(540, 3), 1407, 59]-NRT-code), using

trace code [i] based on linear OOA(64⁷¹, 180, F₆₄, 3, 58) (dual of [(180, 3), 469, 59]-NRT-code), using
- constructionÂ X applied to AG(3;F,469P) âŠ‚ AG(3;F,476P) [i] based on
  1. linear OOA(64⁶⁵, 176, F₆₄, 3, 58) (dual of [(176, 3), 463, 59]-NRT-code), using algebraic-geometric NRT-code AG(3;F,469P) [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(64⁵⁸, 176, F₆₄, 3, 51) (dual of [(176, 3), 470, 52]-NRT-code), using algebraic-geometric NRT-code AG(3;F,476P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177 (see above)
  3. linear OOA(64⁶, 4, F₆₄, 3, 6) (dual of [(4, 3), 6, 7]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(64⁶, 64, F₆₄, 3, 6) (dual of [(64, 3), 186, 7]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(3;186,64) [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.