MinT - Information on Result #982222

Information on Result #982222

Linear OOA(8¹⁷⁰, 193, F₈, 3, 61) (dual of [(193, 3), 409, 62]-NRT-code), using OOA 2-folding based on linear OOA(8¹⁷⁰, 386, F₈, 2, 61) (dual of [(386, 2), 602, 62]-NRT-code), using

trace code [i] based on linear OOA(64⁸⁵, 193, F₆₄, 2, 61) (dual of [(193, 2), 301, 62]-NRT-code), using
- constructionÂ X applied to AG(2;F,290P) âŠ‚ AG(2;F,308P) [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(64⁵⁰, 176, F₆₄, 2, 43) (dual of [(176, 2), 302, 44]-NRT-code), using algebraic-geometric NRT-code AG(2;F,308P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177 (see above)
  3. linear OOA(64¹⁷, 17, F₆₄, 2, 17) (dual of [(17, 2), 17, 18]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(64¹⁷, 64, F₆₄, 2, 17) (dual of [(64, 2), 111, 18]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;111,64) [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.