MinT - Information on Result #1049068

Information on Result #1049068

Linear OOA(4²²³, 168, F₄, 3, 75) (dual of [(168, 3), 281, 76]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(4⁶¹, 38, F₄, 3, 37) (dual of [(38, 3), 53, 38]-NRT-code), using
- constructionÂ X applied to AG(3;F,58P) âŠ‚ AG(3;F,67P) [i] based on
  1. linear OOA(4⁵², 32, F₄, 3, 37) (dual of [(32, 3), 44, 38]-NRT-code), using algebraic-geometric NRT-code AG(3;F,58P) [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
    - an explicitly constructive algebraic function field [i]
  2. linear OOA(4⁴³, 32, F₄, 3, 28) (dual of [(32, 3), 53, 29]-NRT-code), using algebraic-geometric NRT-code AG(3;F,67P) [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33 (see above)
  3. linear OOA(4⁹, 6, F₄, 3, 8) (dual of [(6, 3), 9, 9]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(4⁹, 9, F₄, 3, 8) (dual of [(9, 3), 18, 9]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(3;F,18P) [i] based on function field F/F₄ with g(F) = 1 and N(F) ≥ 9, using
        the Hermitian function field over F₄ [i]
linear OOA(4¹⁶², 130, F₄, 3, 75) (dual of [(130, 3), 228, 76]-NRT-code), using
- extracting embedded OOA [i] based on digital (87, 162, 130)-net over F₄, using
  - trace code for nets [i] based on digital (6, 81, 65)-net over F₁₆, using
    - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
        the Hermitian function field over F₁₆ [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

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(4²²⁴, 168, F₄, 3, 75) (dual of [(168, 3), 280, 76]-NRT-code)	[i]		OOA Duplication