MinT - Information on Result #2770625

Information on Result #2770625

Linear OOA(3¹³⁷, 41, F₃, 4, 100) (dual of [(41, 4), 27, 101]-NRT-code), using strength reduction based on linear OOA(3¹³⁷, 41, F₃, 4, 101) (dual of [(41, 4), 27, 102]-NRT-code), using

constructionÂ X applied to AG(4;F,21P) âŠ‚ AG(4;F,26P) [i] based on
1. linear OOA(3¹²⁷, 36, F₃, 4, 101) (dual of [(36, 4), 17, 102]-NRT-code), using algebraic-geometric NRT-code AG(4;F,21P) with degPÂ =Â 2 [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36, using an explicitly constructive algebraic function field [i]
2. linear OOA(3¹¹⁷, 36, F₃, 4, 91) (dual of [(36, 4), 27, 92]-NRT-code), using algebraic-geometric NRT-code AG(4;F,26P) with degPÂ =Â 2 [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36 (see above)
3. linear OOA(3¹⁰, 5, F₃, 4, 9) (dual of [(5, 4), 10, 10]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(3¹⁰, 7, F₃, 4, 9) (dual of [(7, 4), 18, 10]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(4;F,18P) [i] based on function field F/F₃ with g(F) = 1 and N(F) ≥ 7, 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

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3²¹⁴, 78, F₃, 4, 100) (dual of [(78, 4), 98, 101]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs