MinT - Information on Result #2774663

Information on Result #2774663

Linear OOA(3²⁰⁹, 65, F₃, 4, 123) (dual of [(65, 4), 51, 124]-NRT-code), using strength reduction based on linear OOA(3²⁰⁹, 65, F₃, 4, 124) (dual of [(65, 4), 51, 125]-NRT-code), using

constructionÂ X applied to AG(4;F,63P) âŠ‚ AG(4;F,95P) [i] based on
1. linear OOA(3¹⁶⁹, 47, F₃, 4, 124) (dual of [(47, 4), 19, 125]-NRT-code), using algebraic-geometric NRT-code AG(4;F,63P) [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(3¹³⁷, 47, F₃, 4, 92) (dual of [(47, 4), 51, 93]-NRT-code), using algebraic-geometric NRT-code AG(4;F,95P) [i] based on function field F/F₃ with g(F) = 45 and N(F) ≥ 48 (see above)
3. linear OOA(3⁴⁰, 18, F₃, 4, 31) (dual of [(18, 4), 32, 32]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(3⁴⁰, 19, F₃, 4, 31) (dual of [(19, 4), 36, 32]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(4;F,44P) [i] based on function field F/F₃ with g(F) = 9 and N(F) ≥ 19, 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.