MinT - Information on Result #2510159

Information on Result #2510159

Linear OOA(8¹⁰⁹, 360, F₈, 2, 43) (dual of [(360, 2), 611, 44]-NRT-code), using 8¹ times duplication based on linear OOA(8¹⁰⁸, 360, F₈, 2, 43) (dual of [(360, 2), 612, 44]-NRT-code), using

trace code [i] based on linear OOA(64⁵⁴, 180, F₆₄, 2, 43) (dual of [(180, 2), 306, 44]-NRT-code), using
- constructionÂ X applied to AG(2;F,308P) âŠ‚ AG(2;F,313P) [i] based on
  1. 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, using
    - a function field by GarcÃa and Quoos [i]
  2. linear OOA(64⁴⁵, 176, F₆₄, 2, 38) (dual of [(176, 2), 307, 39]-NRT-code), using algebraic-geometric NRT-code AG(2;F,313P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177 (see above)
  3. linear OOA(64⁴, 4, F₆₄, 2, 4) (dual of [(4, 2), 4, 5]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(64⁴, 64, F₆₄, 2, 4) (dual of [(64, 2), 124, 5]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;124,64) [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.