MinT - Information on Result #2648286

Information on Result #2648286

Linear OOA(9¹⁵⁰, 348, F₉, 3, 63) (dual of [(348, 3), 894, 64]-NRT-code), using strength reduction based on linear OOA(9¹⁵⁰, 348, F₉, 3, 64) (dual of [(348, 3), 894, 65]-NRT-code), using

trace code [i] based on linear OOA(81⁷⁵, 174, F₈₁, 3, 64) (dual of [(174, 3), 447, 65]-NRT-code), using
- constructionÂ X applied to AG(3;F,448P) âŠ‚ AG(3;F,453P) [i] based on
  1. linear OOA(81⁷¹, 171, F₈₁, 3, 64) (dual of [(171, 3), 442, 65]-NRT-code), using algebraic-geometric NRT-code AG(3;F,448P) [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(81⁶⁶, 171, F₈₁, 3, 59) (dual of [(171, 3), 447, 60]-NRT-code), using algebraic-geometric NRT-code AG(3;F,453P) [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.