MinT - Information on Result #2806053

Information on Result #2806053

Linear OOA(3²³⁷, 85, F₃, 4, 111) (dual of [(85, 4), 103, 112]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(3²³³, 84, F₃, 4, 111) (dual of [(84, 4), 103, 112]-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(3⁷⁰, 28, F₃, 4, 55) (dual of [(28, 4), 42, 56]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(4;F,56P) [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28 (see above)
3. linear OOA(3¹¹¹, 28, F₃, 4, 111) (dual of [(28, 4), 1, 112]-NRT-code), using
  - dual of repetition NRT-code with length 28 [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(3²³⁹, 85, F₃, 4, 111) (dual of [(85, 4), 101, 112]-NRT-code)	[i]		OOA Duplication