MinT - Information on Result #2856485

Information on Result #2856485

Linear OOA(3²¹⁹, 58, F₃, 5, 144) (dual of [(58, 5), 71, 145]-NRT-code), using strength reduction based on linear OOA(3²¹⁹, 58, F₃, 5, 145) (dual of [(58, 5), 71, 146]-NRT-code), using

constructionÂ X applied to AG(5;F,89P) âŠ‚ AG(5;F,115P) [i] based on
1. linear OOA(3¹⁹⁰, 47, F₃, 5, 145) (dual of [(47, 5), 45, 146]-NRT-code), using algebraic-geometric NRT-code AG(5;F,89P) [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(3¹⁶⁴, 47, F₃, 5, 119) (dual of [(47, 5), 71, 120]-NRT-code), using algebraic-geometric NRT-code AG(5;F,115P) [i] based on function field F/F₃ with g(F) = 45 and N(F) ≥ 48 (see above)
3. linear OOA(3²⁹, 11, F₃, 5, 25) (dual of [(11, 5), 26, 26]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(3²⁹, 12, F₃, 5, 25) (dual of [(12, 5), 31, 26]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(5;F,34P) [i] based on function field F/F₃ with g(F) = 4 and N(F) ≥ 12, using
      - an explicitly constructive algebraic function field [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.