MinT - Information on Result #982124

Information on Result #982124

Linear OOA(8¹⁴⁴, 182, F₈, 3, 59) (dual of [(182, 3), 402, 60]-NRT-code), using OOA 2-folding based on linear OOA(8¹⁴⁴, 364, F₈, 2, 59) (dual of [(364, 2), 584, 60]-NRT-code), using

trace code [i] based on linear OOA(64⁷², 182, F₆₄, 2, 59) (dual of [(182, 2), 292, 60]-NRT-code), using
- constructionÂ X applied to AG(2;F,292P) âŠ‚ AG(2;F,299P) [i] based on
  1. linear OOA(64⁶⁶, 176, F₆₄, 2, 59) (dual of [(176, 2), 286, 60]-NRT-code), using algebraic-geometric NRT-code AG(2;F,292P) [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(64⁵⁹, 176, F₆₄, 2, 52) (dual of [(176, 2), 293, 53]-NRT-code), using algebraic-geometric NRT-code AG(2;F,299P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177 (see above)
  3. linear OOA(64⁶, 6, F₆₄, 2, 6) (dual of [(6, 2), 6, 7]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(64⁶, 64, F₆₄, 2, 6) (dual of [(64, 2), 122, 7]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;122,64) [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.