MinT - Information on Result #2806065

Information on Result #2806065

Linear OOA(3²⁴², 86, F₃, 4, 112) (dual of [(86, 4), 102, 113]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(3²³⁸, 85, F₃, 4, 112) (dual of [(85, 4), 102, 113]-NRT-code), using

strength reduction [i] based on linear OOA(3²³⁸, 85, F₃, 4, 113) (dual of [(85, 4), 102, 114]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(3⁵², 28, F₃, 4, 37) (dual of [(28, 4), 60, 38]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(4;F,74P) [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28, using
      - an explicitly constructive algebraic function field [i]
  2. linear OOA(3⁷¹, 28, F₃, 4, 56) (dual of [(28, 4), 41, 57]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(4;F,55P) [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28 (see above)
  3. linear OOA(3¹¹⁵, 29, F₃, 4, 113) (dual of [(29, 4), 1, 114]-NRT-code), using
    - strength reduction [i] based on linear OOA(3¹¹⁵, 29, F₃, 4, 115) (dual of [(29, 4), 1, 116]-NRT-code), using
      - dual of repetition NRT-code with length 29 [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(3²⁴³, 86, F₃, 4, 112) (dual of [(86, 4), 101, 113]-NRT-code)	[i]		OOA Duplication