MinT - Information on Result #1049094

Information on Result #1049094

Linear OOA(4²³⁶, 165, F₄, 3, 82) (dual of [(165, 3), 259, 83]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(4⁶⁰, 35, F₄, 3, 41) (dual of [(35, 3), 45, 42]-NRT-code), using
- constructionÂ X applied to AG(3;F,54P) âŠ‚ AG(3;F,59P) [i] based on
  1. linear OOA(4⁵⁶, 32, F₄, 3, 41) (dual of [(32, 3), 40, 42]-NRT-code), using algebraic-geometric NRT-code AG(3;F,54P) [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(4⁵¹, 32, F₄, 3, 36) (dual of [(32, 3), 45, 37]-NRT-code), using algebraic-geometric NRT-code AG(3;F,59P) [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33 (see above)
  3. linear OOA(4⁴, 3, F₄, 3, 4) (dual of [(3, 3), 5, 5]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(4⁴, 4, F₄, 3, 4) (dual of [(4, 3), 8, 5]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(3;8,4) [i]
linear OOA(4¹⁷⁶, 130, F₄, 3, 82) (dual of [(130, 3), 214, 83]-NRT-code), using
- extracting embedded OOA [i] based on digital (94, 176, 130)-net over F₄, using
  - trace code for nets [i] based on digital (6, 88, 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(4²³⁷, 165, F₄, 3, 82) (dual of [(165, 3), 258, 83]-NRT-code)	[i]		OOA Duplication