MinT - Information on Result #1104248

Information on Result #1104248

Linear OOA(3¹¹², 26, F₃, 5, 59) (dual of [(26, 5), 18, 60]-NRT-code), using OOA 2-folding based on linear OOA(3¹¹², 52, F₃, 3, 59) (dual of [(52, 3), 44, 60]-NRT-code), using

constructionÂ X applied to AG(3;F,81P) âŠ‚ AG(3;F,89P) [i] based on
1. linear OOA(3¹⁰⁴, 47, F₃, 3, 59) (dual of [(47, 3), 37, 60]-NRT-code), using algebraic-geometric NRT-code AG(3;F,81P) [i] based on function field F/F₃ with g(F) = 45 and N(F) ≥ 48, using
  - an explicitly constructive algebraic function field [i]
2. linear OOA(3⁹⁶, 47, F₃, 3, 51) (dual of [(47, 3), 45, 52]-NRT-code), using algebraic-geometric NRT-code AG(3;F,89P) [i] based on function field F/F₃ with g(F) = 45 and N(F) ≥ 48 (see above)
3. linear OOA(3⁸, 5, F₃, 3, 7) (dual of [(5, 3), 7, 8]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(3⁸, 7, F₃, 3, 7) (dual of [(7, 3), 13, 8]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,13P) [i] based on function field F/F₃ with g(F) = 1 and N(F) ≥ 7, using
      - an explicitly constructive algebraic function field [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.