MinT - Information on Result #2651957

Information on Result #2651957

Linear OOA(2⁶⁸, 24, F₂, 3, 50) (dual of [(24, 3), 4, 51]-NRT-code), using 6 step truncation based on linear OOA(2⁷⁴, 26, F₂, 3, 56) (dual of [(26, 3), 4, 57]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(2¹¹, 5, F₂, 3, 10) (dual of [(5, 3), 4, 11]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,4P) [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(2⁵⁹, 21, F₂, 3, 45) (dual of [(21, 3), 4, 46]-NRT-code), using
  - juxtaposition [i] based on
    1. linear OOA(2¹¹, 5, F₂, 3, 10) (dual of [(5, 3), 4, 11]-NRT-code) (see above)
    2. linear OOA(2⁴⁴, 16, F₂, 3, 34) (dual of [(16, 3), 4, 35]-NRT-code), using
      - juxtaposition [i] based on
        linear OOA(2¹¹, 5, F₂, 3, 10) (dual of [(5, 3), 4, 11]-NRT-code) (see above)
        linear OOA(2²⁹, 11, F₂, 3, 23) (dual of [(11, 3), 4, 24]-NRT-code), using
        juxtaposition [i] based on
        linear OOA(2¹¹, 5, F₂, 3, 10) (dual of [(5, 3), 4, 11]-NRT-code) (see above)
        linear OOA(2¹⁴, 6, F₂, 3, 12) (dual of [(6, 3), 4, 13]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(3;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(2⁶⁸, 12, F₂, 6, 50) (dual of [(12, 6), 4, 51]-NRT-code)	[i]		OOA Folding