MinT - Information on Result #2758625

Information on Result #2758625

Linear OOA(2⁸⁴, 22, F₂, 4, 66) (dual of [(22, 4), 4, 67]-NRT-code), using strength reduction based on linear OOA(2⁸⁴, 22, F₂, 4, 68) (dual of [(22, 4), 4, 69]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(2¹², 4, F₂, 4, 11) (dual of [(4, 4), 4, 12]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(2¹², 5, F₂, 4, 11) (dual of [(5, 4), 8, 12]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(4;F,8P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, using
      - an explicitly constructive algebraic function field [i]
2. linear OOA(2⁶⁸, 18, F₂, 4, 56) (dual of [(18, 4), 4, 57]-NRT-code), using
  - repeating each code word 3 times [i] based on linear OOA(2²⁰, 6, F₂, 4, 18) (dual of [(6, 4), 4, 19]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(4;F,5P) [i] based on function field F/F₂ with g(F) = 2 and N(F) ≥ 6, 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(2⁸⁴, 11, F₂, 8, 66) (dual of [(11, 8), 4, 67]-NRT-code)	[i]		OOA Folding