MinT - Information on Result #2670409

Information on Result #2670409

Linear OOA(2²²⁴, 210, F₂, 3, 51) (dual of [(210, 3), 406, 52]-NRT-code), using 2² times duplication based on linear OOA(2²²², 210, F₂, 3, 51) (dual of [(210, 3), 408, 52]-NRT-code), using

trace code [i] based on linear OOA(8⁷⁴, 70, F₈, 3, 51) (dual of [(70, 3), 136, 52]-NRT-code), using
- constructionÂ X applied to AG(3;F,140P) âŠ‚ AG(3;F,150P) [i] based on
  1. linear OOA(8⁶⁵, 64, F₈, 3, 51) (dual of [(64, 3), 127, 52]-NRT-code), using algebraic-geometric NRT-code AG(3;F,140P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
    - the Suzuki function field over F₈ [i]
  2. linear OOA(8⁵⁵, 64, F₈, 3, 41) (dual of [(64, 3), 137, 42]-NRT-code), using algebraic-geometric NRT-code AG(3;F,150P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
  3. linear OOA(8⁹, 6, F₈, 3, 9) (dual of [(6, 3), 9, 10]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(8⁹, 8, F₈, 3, 9) (dual of [(8, 3), 15, 10]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(3;15,8) [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.