MinT - Information on Result #2514145

Information on Result #2514145

Linear OOA(9¹¹⁷, 350, F₉, 2, 47) (dual of [(350, 2), 583, 48]-NRT-code), using 9¹ times duplication based on linear OOA(9¹¹⁶, 350, F₉, 2, 47) (dual of [(350, 2), 584, 48]-NRT-code), using

trace code [i] based on linear OOA(81⁵⁸, 175, F₈₁, 2, 47) (dual of [(175, 2), 292, 48]-NRT-code), using
- constructionÂ X applied to AG(2;F,294P) âŠ‚ AG(2;F,299P) [i] based on
  1. linear OOA(81⁵⁴, 171, F₈₁, 2, 47) (dual of [(171, 2), 288, 48]-NRT-code), using algebraic-geometric NRT-code AG(2;F,294P) [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(81⁴⁹, 171, F₈₁, 2, 42) (dual of [(171, 2), 293, 43]-NRT-code), using algebraic-geometric NRT-code AG(2;F,299P) [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.