MinT - Information on Result #2769978

Information on Result #2769978

Linear OOA(3¹¹⁷, 53, F₃, 4, 59) (dual of [(53, 4), 95, 60]-NRT-code), using strength reduction based on linear OOA(3¹¹⁷, 53, F₃, 4, 60) (dual of [(53, 4), 95, 61]-NRT-code), using

constructionÂ X applied to AG(4;F,127P) âŠ‚ AG(4;F,139P) [i] based on
1. linear OOA(3¹⁰⁵, 47, F₃, 4, 60) (dual of [(47, 4), 83, 61]-NRT-code), using algebraic-geometric NRT-code AG(4;F,127P) [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(3⁹³, 47, F₃, 4, 48) (dual of [(47, 4), 95, 49]-NRT-code), using algebraic-geometric NRT-code AG(4;F,139P) [i] based on function field F/F₃ with g(F) = 45 and N(F) ≥ 48 (see above)
3. linear OOA(3¹², 6, F₃, 4, 11) (dual of [(6, 4), 12, 12]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(3¹², 7, F₃, 4, 11) (dual of [(7, 4), 16, 12]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(4;F,16P) [i] based on function field F/F₃ with g(F) = 1 and N(F) ≥ 7, 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.