MinT - Information on Result #2761463

Information on Result #2761463

Linear OOA(2¹⁵⁰, 39, F₂, 4, 110) (dual of [(39, 4), 6, 111]-NRT-code), using strength reduction based on linear OOA(2¹⁵⁰, 39, F₂, 4, 112) (dual of [(39, 4), 6, 113]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(2³⁰, 9, F₂, 4, 25) (dual of [(9, 4), 6, 26]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(4;F,10P) [i] based on function field F/F₂ with g(F) = 5 and N(F) ≥ 9, using
    - an explicitly constructive algebraic function field [i]
2. linear OOA(2¹¹⁴, 30, F₂, 4, 86) (dual of [(30, 4), 6, 87]-NRT-code), using
  - repeating each code word 3 times [i] based on linear OOA(2³⁴, 10, F₂, 4, 28) (dual of [(10, 4), 6, 29]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(4;F,11P) [i] based on function field F/F₂ with g(F) = 6 and N(F) ≥ 10, 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(2²⁵⁹, 76, F₂, 4, 110) (dual of [(76, 4), 45, 111]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs