MinT - Information on Result #2647252

Information on Result #2647252

Linear OOA(9¹⁰⁸, 348, F₉, 3, 42) (dual of [(348, 3), 936, 43]-NRT-code), using strength reduction based on linear OOA(9¹⁰⁸, 348, F₉, 3, 43) (dual of [(348, 3), 936, 44]-NRT-code), using

trace code [i] based on linear OOA(81⁵⁴, 174, F₈₁, 3, 43) (dual of [(174, 3), 468, 44]-NRT-code), using
- constructionÂ X applied to AG(3;F,469P) âŠ‚ AG(3;F,474P) [i] based on
  1. linear OOA(81⁵⁰, 171, F₈₁, 3, 43) (dual of [(171, 3), 463, 44]-NRT-code), using algebraic-geometric NRT-code AG(3;F,469P) [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(81⁴⁵, 171, F₈₁, 3, 38) (dual of [(171, 3), 468, 39]-NRT-code), using algebraic-geometric NRT-code AG(3;F,474P) [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172 (see above)
  3. linear OOA(81⁴, 3, F₈₁, 3, 4) (dual of [(3, 3), 5, 5]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(81⁴, 81, F₈₁, 3, 4) (dual of [(81, 3), 239, 5]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(3;239,81) [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.