MinT - Information on Result #2640266

Information on Result #2640266

Linear OOA(5¹⁰⁴, 85, F₅, 3, 53) (dual of [(85, 3), 151, 54]-NRT-code), using strength reduction based on linear OOA(5¹⁰⁴, 85, F₅, 3, 54) (dual of [(85, 3), 151, 55]-NRT-code), using

constructionÂ X applied to AG(3;F,176P) âŠ‚ AG(3;F,188P) [i] based on
1. linear OOA(5⁹², 77, F₅, 3, 54) (dual of [(77, 3), 139, 55]-NRT-code), using algebraic-geometric NRT-code AG(3;F,176P) [i] based on function field F/F₅ with g(F) = 38 and N(F) ≥ 78, using
  - an explicitly constructive algebraic function field [i]
2. linear OOA(5⁸⁰, 77, F₅, 3, 42) (dual of [(77, 3), 151, 43]-NRT-code), using algebraic-geometric NRT-code AG(3;F,188P) [i] based on function field F/F₅ with g(F) = 38 and N(F) ≥ 78 (see above)
3. linear OOA(5¹², 8, F₅, 3, 11) (dual of [(8, 3), 12, 12]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(5¹², 10, F₅, 3, 11) (dual of [(10, 3), 18, 12]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,18P) [i] based on function field F/F₅ with g(F) = 1 and N(F) ≥ 10, 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.