MinT - Information on Result #908859

Information on Result #908859

Linear OOA(2¹²⁹, 67, F₂, 2, 74) (dual of [(67, 2), 5, 75]-NRT-code), using juxtaposition based on

linear OOA(2¹¹, 8, F₂, 2, 8) (dual of [(8, 2), 5, 9]-NRT-code), using
- an explicit generator matrix by Edel [i]
linear OOA(2¹¹³, 59, F₂, 2, 65) (dual of [(59, 2), 5, 66]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(2¹¹, 8, F₂, 2, 8) (dual of [(8, 2), 5, 9]-NRT-code) (see above)
  2. linear OOA(2⁹⁷, 51, F₂, 2, 56) (dual of [(51, 2), 5, 57]-NRT-code), using
    - juxtaposition [i] based on
      1. linear OOA(2¹¹, 8, F₂, 2, 8) (dual of [(8, 2), 5, 9]-NRT-code) (see above)
      2. linear OOA(2⁸¹, 43, F₂, 2, 47) (dual of [(43, 2), 5, 48]-NRT-code), using
        juxtaposition [i] based on
        linear OOA(2¹¹, 8, F₂, 2, 8) (dual of [(8, 2), 5, 9]-NRT-code) (see above)
        linear OOA(2⁶⁵, 35, F₂, 2, 38) (dual of [(35, 2), 5, 39]-NRT-code), using
        juxtaposition [i] based on
        linear OOA(2¹¹, 8, F₂, 2, 8) (dual of [(8, 2), 5, 9]-NRT-code) (see above)
        linear OOA(2⁴⁹, 27, F₂, 2, 29) (dual of [(27, 2), 5, 30]-NRT-code), using
        juxtaposition [i] based on
        linear OOA(2¹¹, 8, F₂, 2, 8) (dual of [(8, 2), 5, 9]-NRT-code) (see above)
        linear OOA(2³³, 19, F₂, 2, 20) (dual of [(19, 2), 5, 21]-NRT-code), using
        juxtaposition [i] based on
        linear OOA(2¹¹, 8, F₂, 2, 8) (dual of [(8, 2), 5, 9]-NRT-code) (see above)
        linear OOA(2¹⁷, 11, F₂, 2, 11) (dual of [(11, 2), 5, 12]-NRT-code), using
        (u,Â u+v)-construction [i] based on
        linear OOA(2⁶, 5, F₂, 2, 5) (dual of [(5, 2), 4, 6]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(2;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]
        linear OOA(2¹¹, 6, F₂, 2, 11) (dual of [(6, 2), 1, 12]-NRT-code), using
        dual of repetition NRT-code with length 6 [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(2¹⁴⁵, 75, F₂, 2, 83) (dual of [(75, 2), 5, 84]-NRT-code)	[i]		Juxtaposition for OOAs