MinT - Information on Result #2857003

Information on Result #2857003

Linear OOA(3²²⁶, 56, F₃, 5, 156) (dual of [(56, 5), 54, 157]-NRT-code), using strength reduction based on linear OOA(3²²⁶, 56, F₃, 5, 157) (dual of [(56, 5), 54, 158]-NRT-code), using

constructionÂ X applied to AG(5;F,77P) âŠ‚ AG(5;F,99P) [i] based on
1. linear OOA(3²⁰², 47, F₃, 5, 157) (dual of [(47, 5), 33, 158]-NRT-code), using algebraic-geometric NRT-code AG(5;F,77P) [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(3¹⁸⁰, 47, F₃, 5, 135) (dual of [(47, 5), 55, 136]-NRT-code), using algebraic-geometric NRT-code AG(5;F,99P) [i] based on function field F/F₃ with g(F) = 45 and N(F) ≥ 48 (see above)
3. linear OOA(3²⁴, 9, F₃, 5, 21) (dual of [(9, 5), 21, 22]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(3²⁴, 10, F₃, 5, 21) (dual of [(10, 5), 26, 22]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(5;F,28P) [i] based on function field F/F₃ with g(F) = 3 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.