MinT - Information on Result #2795262

Information on Result #2795262

Linear OOA(2¹⁷¹, 53, F₂, 4, 90) (dual of [(53, 4), 41, 91]-NRT-code), using 2¹ times duplication based on linear OOA(2¹⁷⁰, 53, F₂, 4, 90) (dual of [(53, 4), 42, 91]-NRT-code), using

strength reduction [i] based on linear OOA(2¹⁷⁰, 53, F₂, 4, 91) (dual of [(53, 4), 42, 92]-NRT-code), using
- constructionÂ X applied to AG(4;F,50P) âŠ‚ AG(4;F,55P) [i] based on
  1. linear OOA(2¹⁶⁰, 48, F₂, 4, 91) (dual of [(48, 4), 32, 92]-NRT-code), using algebraic-geometric NRT-code AG(4;F,50P) with degPÂ =Â 2 [i] based on function field F/F₂ with g(F) = 69 and N(F) ≥ 48, using an explicitly constructive algebraic function field [i]
  2. linear OOA(2¹⁵⁰, 48, F₂, 4, 81) (dual of [(48, 4), 42, 82]-NRT-code), using algebraic-geometric NRT-code AG(4;F,55P) with degPÂ =Â 2 [i] based on function field F/F₂ with g(F) = 69 and N(F) ≥ 48 (see above)
  3. linear OOA(2¹⁰, 5, F₂, 4, 9) (dual of [(5, 4), 10, 10]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(4;F,10P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, 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.