MinT - Information on Result #2768341

Information on Result #2768341

Linear OOA(2²⁶⁰, 66, F₂, 4, 209) (dual of [(66, 4), 4, 210]-NRT-code), using strength reduction based on linear OOA(2²⁶⁰, 66, F₂, 4, 210) (dual of [(66, 4), 4, 211]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(2¹⁶, 5, F₂, 4, 15) (dual of [(5, 4), 4, 16]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(4;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(2²⁴⁰, 61, F₂, 4, 194) (dual of [(61, 4), 4, 195]-NRT-code), using
  - juxtaposition [i] based on
    1. linear OOA(2¹⁶, 5, F₂, 4, 15) (dual of [(5, 4), 4, 16]-NRT-code) (see above)
    2. linear OOA(2²²⁰, 56, F₂, 4, 178) (dual of [(56, 4), 4, 179]-NRT-code), using
      - juxtaposition [i] based on
        linear OOA(2¹⁶, 5, F₂, 4, 15) (dual of [(5, 4), 4, 16]-NRT-code) (see above)
        linear OOA(2²⁰⁰, 51, F₂, 4, 162) (dual of [(51, 4), 4, 163]-NRT-code), using
        juxtaposition [i] based on
        linear OOA(2¹⁶, 5, F₂, 4, 15) (dual of [(5, 4), 4, 16]-NRT-code) (see above)
        linear OOA(2¹⁸⁰, 46, F₂, 4, 146) (dual of [(46, 4), 4, 147]-NRT-code), using
        juxtaposition [i] based on
        linear OOA(2¹⁶, 5, F₂, 4, 15) (dual of [(5, 4), 4, 16]-NRT-code) (see above)
        linear OOA(2¹⁶⁰, 41, F₂, 4, 130) (dual of [(41, 4), 4, 131]-NRT-code), using
        juxtaposition [i] based on
        linear OOA(2¹⁶, 5, F₂, 4, 15) (dual of [(5, 4), 4, 16]-NRT-code) (see above)
        linear OOA(2¹⁴⁰, 36, F₂, 4, 114) (dual of [(36, 4), 4, 115]-NRT-code), using
        juxtaposition [i] based on
        linear OOA(2¹⁶, 5, F₂, 4, 15) (dual of [(5, 4), 4, 16]-NRT-code) (see above)
        linear OOA(2¹²⁰, 31, F₂, 4, 98) (dual of [(31, 4), 4, 99]-NRT-code), using
        juxtaposition [i] based on
        linear OOA(2¹⁶, 5, F₂, 4, 15) (dual of [(5, 4), 4, 16]-NRT-code) (see above)
        linear OOA(2¹⁰⁰, 26, F₂, 4, 82) (dual of [(26, 4), 4, 83]-NRT-code), using
        juxtaposition [i] based on
        linear OOA(2¹⁶, 5, F₂, 4, 15) (dual of [(5, 4), 4, 16]-NRT-code) (see above)
        linear OOA(2⁸⁰, 21, F₂, 4, 66) (dual of [(21, 4), 4, 67]-NRT-code), using
        juxtaposition [i] based on
        linear OOA(2¹⁶, 5, F₂, 4, 15) (dual of [(5, 4), 4, 16]-NRT-code) (see above)
        linear OOA(2⁶⁰, 16, F₂, 4, 50) (dual of [(16, 4), 4, 51]-NRT-code), using
        juxtaposition [i] based on
        linear OOA(2¹⁶, 5, F₂, 4, 15) (dual of [(5, 4), 4, 16]-NRT-code) (see above)
        linear OOA(2⁴⁰, 11, F₂, 4, 34) (dual of [(11, 4), 4, 35]-NRT-code), using
        juxtaposition [i] based on
        linear OOA(2¹⁶, 5, F₂, 4, 15) (dual of [(5, 4), 4, 16]-NRT-code) (see above)
        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		Method
1	Linear OOA(2²⁵³, 64, F₂, 4, 202) (dual of [(64, 4), 3, 203]-NRT-code)	[i]	Truncation for OOAs
2	Linear OOA(2²⁵², 64, F₂, 4, 201) (dual of [(64, 4), 4, 202]-NRT-code)	[i]
3	Linear OOA(2²³³, 59, F₂, 4, 182) (dual of [(59, 4), 3, 183]-NRT-code)	[i]
4	Linear OOA(2²³², 59, F₂, 4, 181) (dual of [(59, 4), 4, 182]-NRT-code)	[i]
5	Linear OOA(2²⁶⁰, 33, F₂, 8, 209) (dual of [(33, 8), 4, 210]-NRT-code)	[i]	OOA Folding