MinT - Information on Result #2774712

Information on Result #2774712

Linear OOA(3²¹⁰, 70, F₃, 4, 112) (dual of [(70, 4), 70, 113]-NRT-code), using strength reduction based on linear OOA(3²¹⁰, 70, F₃, 4, 113) (dual of [(70, 4), 70, 114]-NRT-code), using

constructionÂ X applied to AG(4;F,74P) âŠ‚ AG(4;F,114P) [i] based on
1. linear OOA(3¹⁵⁸, 47, F₃, 4, 113) (dual of [(47, 4), 30, 114]-NRT-code), using algebraic-geometric NRT-code AG(4;F,74P) [i] based on function field F/F₃ with g(F) = 45 and N(F) ≥ 48, using
  - an explicitly constructive algebraic function field [i]
2. linear OOA(3¹¹⁸, 47, F₃, 4, 73) (dual of [(47, 4), 70, 74]-NRT-code), using algebraic-geometric NRT-code AG(4;F,114P) [i] based on function field F/F₃ with g(F) = 45 and N(F) ≥ 48 (see above)
3. linear OOA(3⁵², 23, F₃, 4, 39) (dual of [(23, 4), 40, 40]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(3⁵², 24, F₃, 4, 39) (dual of [(24, 4), 44, 40]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(4;F,56P) [i] based on function field F/F₃ with g(F) = 13 and N(F) ≥ 24, using
      - a function field by SÃ©mirat [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.