MinT - Information on Result #1097807

Information on Result #1097807

Linear OOA(2¹²², 35, F₂, 5, 42) (dual of [(35, 5), 53, 43]-NRT-code), using OOA 2-folding based on linear OOA(2¹²², 70, F₂, 3, 42) (dual of [(70, 3), 88, 43]-NRT-code), using

trace code [i] based on linear OOA(4⁶¹, 35, F₄, 3, 42) (dual of [(35, 3), 44, 43]-NRT-code), using
- constructionÂ X applied to AG(3;F,53P) âŠ‚ AG(3;F,58P) [i] based on
  1. linear OOA(4⁵⁷, 32, F₄, 3, 42) (dual of [(32, 3), 39, 43]-NRT-code), using algebraic-geometric NRT-code AG(3;F,53P) [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
    - an explicitly constructive algebraic function field [i]
  2. linear OOA(4⁵², 32, F₄, 3, 37) (dual of [(32, 3), 44, 38]-NRT-code), using algebraic-geometric NRT-code AG(3;F,58P) [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33 (see above)
  3. linear OOA(4⁴, 3, F₄, 3, 4) (dual of [(3, 3), 5, 5]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(4⁴, 4, F₄, 3, 4) (dual of [(4, 3), 8, 5]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(3;8,4) [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.