MinT - Information on Result #2514144

Information on Result #2514144

Linear OOA(9¹¹⁵, 348, F₉, 2, 47) (dual of [(348, 2), 581, 48]-NRT-code), using 9¹ times duplication based on linear OOA(9¹¹⁴, 348, F₉, 2, 47) (dual of [(348, 2), 582, 48]-NRT-code), using

trace code [i] based on linear OOA(81⁵⁷, 174, F₈₁, 2, 47) (dual of [(174, 2), 291, 48]-NRT-code), using
- constructionÂ X applied to AG(2;F,294P) âŠ‚ AG(2;F,298P) [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(81⁵⁰, 171, F₈₁, 2, 43) (dual of [(171, 2), 292, 44]-NRT-code), using algebraic-geometric NRT-code AG(2;F,298P) [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172 (see above)
  3. linear OOA(81³, 3, F₈₁, 2, 3) (dual of [(3, 2), 3, 4]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(81³, 81, F₈₁, 2, 3) (dual of [(81, 2), 159, 4]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;159,81) [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.