MinT - Information on Result #1103248

Information on Result #1103248

Linear OOA(3⁷⁷, 21, F₃, 5, 41) (dual of [(21, 5), 28, 42]-NRT-code), using OOA 2-folding based on linear OOA(3⁷⁷, 42, F₃, 3, 41) (dual of [(42, 3), 49, 42]-NRT-code), using

constructionÂ X applied to AG(3;F,33P) âŠ‚ AG(3;F,38P) [i] based on
1. linear OOA(3⁶⁷, 36, F₃, 3, 41) (dual of [(36, 3), 41, 42]-NRT-code), using algebraic-geometric NRT-code AG(3;F,33P) with degPÂ =Â 2 [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36, using an explicitly constructive algebraic function field [i]
2. linear OOA(3⁵⁷, 36, F₃, 3, 31) (dual of [(36, 3), 51, 32]-NRT-code), using algebraic-geometric NRT-code AG(3;F,38P) with degPÂ =Â 2 [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36 (see above)
3. linear OOA(3¹⁰, 6, F₃, 3, 9) (dual of [(6, 3), 8, 10]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(3¹⁰, 7, F₃, 3, 9) (dual of [(7, 3), 11, 10]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,11P) [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.