MinT - Information on Result #982221

Information on Result #982221

Linear OOA(8¹⁶⁸, 192, F₈, 3, 61) (dual of [(192, 3), 408, 62]-NRT-code), using OOA 2-folding based on linear OOA(8¹⁶⁸, 384, F₈, 2, 61) (dual of [(384, 2), 600, 62]-NRT-code), using

trace code [i] based on linear OOA(64⁸⁴, 192, F₆₄, 2, 61) (dual of [(192, 2), 300, 62]-NRT-code), using
- constructionÂ X applied to AG(2;F,290P) âŠ‚ AG(2;F,307P) [i] based on
  1. linear OOA(64⁶⁸, 176, F₆₄, 2, 61) (dual of [(176, 2), 284, 62]-NRT-code), using algebraic-geometric NRT-code AG(2;F,290P) [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(64⁵¹, 176, F₆₄, 2, 44) (dual of [(176, 2), 301, 45]-NRT-code), using algebraic-geometric NRT-code AG(2;F,307P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177 (see above)
  3. linear OOA(64¹⁶, 16, F₆₄, 2, 16) (dual of [(16, 2), 16, 17]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(64¹⁶, 64, F₆₄, 2, 16) (dual of [(64, 2), 112, 17]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;112,64) [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.