MinT - Information on Result #2794597

Information on Result #2794597

Linear OOA(2¹⁵⁷, 53, F₂, 4, 77) (dual of [(53, 4), 55, 78]-NRT-code), using 2¹ times duplication based on linear OOA(2¹⁵⁶, 53, F₂, 4, 77) (dual of [(53, 4), 56, 78]-NRT-code), using

constructionÂ X applied to AG(4;F,57P) âŠ‚ AG(4;F,62P) [i] based on
1. linear OOA(2¹⁴⁶, 48, F₂, 4, 77) (dual of [(48, 4), 46, 78]-NRT-code), using algebraic-geometric NRT-code AG(4;F,57P) 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(2¹³⁶, 48, F₂, 4, 67) (dual of [(48, 4), 56, 68]-NRT-code), using algebraic-geometric NRT-code AG(4;F,62P) 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.