MinT - Information on Result #1064601

Information on Result #1064601

Linear OOA(3²⁴³, 150, F₃, 4, 65) (dual of [(150, 4), 357, 66]-NRT-code), using OOA 2-folding based on linear OOA(3²⁴³, 300, F₃, 2, 65) (dual of [(300, 2), 357, 66]-NRT-code), using

trace code [i] based on linear OOA(27⁸¹, 100, F₂₇, 2, 65) (dual of [(100, 2), 119, 66]-NRT-code), using
- constructionÂ X applied to AG(2;F,124P) âŠ‚ AG(2;F,130P) [i] based on
  1. linear OOA(27⁷⁶, 95, F₂₇, 2, 65) (dual of [(95, 2), 114, 66]-NRT-code), using algebraic-geometric NRT-code AG(2;F,124P) [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
    - an explicitly constructive algebraic function field [i]
  2. linear OOA(27⁷⁰, 95, F₂₇, 2, 59) (dual of [(95, 2), 120, 60]-NRT-code), using algebraic-geometric NRT-code AG(2;F,130P) [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96 (see above)
  3. linear OOA(27⁵, 5, F₂₇, 2, 5) (dual of [(5, 2), 5, 6]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(27⁵, 27, F₂₇, 2, 5) (dual of [(27, 2), 49, 6]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;49,27) [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.