MinT - Information on Result #2775061

Information on Result #2775061

Linear OOA(3²¹⁵, 65, F₃, 4, 129) (dual of [(65, 4), 45, 130]-NRT-code), using strength reduction based on linear OOA(3²¹⁵, 65, F₃, 4, 130) (dual of [(65, 4), 45, 131]-NRT-code), using

constructionÂ X applied to AG(4;F,57P) âŠ‚ AG(4;F,89P) [i] based on
1. linear OOA(3¹⁷⁵, 47, F₃, 4, 130) (dual of [(47, 4), 13, 131]-NRT-code), using algebraic-geometric NRT-code AG(4;F,57P) [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(3¹⁴³, 47, F₃, 4, 98) (dual of [(47, 4), 45, 99]-NRT-code), using algebraic-geometric NRT-code AG(4;F,89P) [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.