MinT - Information on Result #982510

Information on Result #982510

Linear OOA(8¹⁰², 41, F₈, 3, 69) (dual of [(41, 3), 21, 70]-NRT-code), using OOA 2-folding based on linear OOA(8¹⁰², 82, F₈, 2, 69) (dual of [(82, 2), 62, 70]-NRT-code), using

constructionÂ X applied to AG(2;F,58P) âŠ‚ AG(2;F,75P) [i] based on
1. linear OOA(8⁸³, 64, F₈, 2, 69) (dual of [(64, 2), 45, 70]-NRT-code), using algebraic-geometric NRT-code AG(2;F,58P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
  - the Suzuki function field over F₈ [i]
2. linear OOA(8⁶⁶, 64, F₈, 2, 52) (dual of [(64, 2), 62, 53]-NRT-code), using algebraic-geometric NRT-code AG(2;F,75P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
3. linear OOA(8¹⁹, 18, F₈, 2, 16) (dual of [(18, 2), 17, 17]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(8¹⁹, 24, F₈, 2, 16) (dual of [(24, 2), 29, 17]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,31P) [i] based on function field F/F₈ with g(F) = 3 and N(F) ≥ 24, using
      - the Klein quartic over F₈ [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.