MinT - Information on Result #987096

Information on Result #987096

Linear OOA(9¹³⁶, 175, F₉, 3, 57) (dual of [(175, 3), 389, 58]-NRT-code), using OOA 2-folding based on linear OOA(9¹³⁶, 350, F₉, 2, 57) (dual of [(350, 2), 564, 58]-NRT-code), using

trace code [i] based on linear OOA(81⁶⁸, 175, F₈₁, 2, 57) (dual of [(175, 2), 282, 58]-NRT-code), using
- constructionÂ X applied to AG(2;F,284P) âŠ‚ AG(2;F,289P) [i] based on
  1. linear OOA(81⁶⁴, 171, F₈₁, 2, 57) (dual of [(171, 2), 278, 58]-NRT-code), using algebraic-geometric NRT-code AG(2;F,284P) [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
    - a function field by SÃ©mirat [i]
  2. linear OOA(81⁵⁹, 171, F₈₁, 2, 52) (dual of [(171, 2), 283, 53]-NRT-code), using algebraic-geometric NRT-code AG(2;F,289P) [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172 (see above)
  3. linear OOA(81⁴, 4, F₈₁, 2, 4) (dual of [(4, 2), 4, 5]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(81⁴, 81, F₈₁, 2, 4) (dual of [(81, 2), 158, 5]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;158,81) [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.