MinT - Information on Result #1146238

Information on Result #1146238

Linear OOA(2²¹², 36, F₂, 6, 186) (dual of [(36, 6), 4, 187]-NRT-code), using juxtaposition based on

linear OOA(2²⁶, 5, F₂, 6, 25) (dual of [(5, 6), 4, 26]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(6;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(2¹⁸², 31, F₂, 6, 160) (dual of [(31, 6), 4, 161]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(2²⁶, 5, F₂, 6, 25) (dual of [(5, 6), 4, 26]-NRT-code) (see above)
  2. linear OOA(2¹⁵², 26, F₂, 6, 134) (dual of [(26, 6), 4, 135]-NRT-code), using
    - juxtaposition [i] based on
      1. linear OOA(2²⁶, 5, F₂, 6, 25) (dual of [(5, 6), 4, 26]-NRT-code) (see above)
      2. linear OOA(2¹²², 21, F₂, 6, 108) (dual of [(21, 6), 4, 109]-NRT-code), using
        juxtaposition [i] based on
        linear OOA(2²⁶, 5, F₂, 6, 25) (dual of [(5, 6), 4, 26]-NRT-code) (see above)
        linear OOA(2⁹², 16, F₂, 6, 82) (dual of [(16, 6), 4, 83]-NRT-code), using
        juxtaposition [i] based on
        linear OOA(2²⁶, 5, F₂, 6, 25) (dual of [(5, 6), 4, 26]-NRT-code) (see above)
        linear OOA(2⁶², 11, F₂, 6, 56) (dual of [(11, 6), 4, 57]-NRT-code), using
        juxtaposition [i] based on
        linear OOA(2²⁶, 5, F₂, 6, 25) (dual of [(5, 6), 4, 26]-NRT-code) (see above)
        linear OOA(2³², 6, F₂, 6, 30) (dual of [(6, 6), 4, 31]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(6;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(2²¹¹, 35, F₂, 6, 185)	[i]	Truncation for OOAs
2	Linear OOA(2²⁰⁵, 34, F₂, 6, 179)	[i]
3	Linear OOA(2²⁰¹, 34, F₂, 6, 175) (dual of [(34, 6), 3, 176]-NRT-code)	[i]
4	Linear OOA(2²⁰⁰, 34, F₂, 6, 174) (dual of [(34, 6), 4, 175]-NRT-code)	[i]
5	Linear OOA(2¹⁹⁹, 33, F₂, 6, 173)	[i]
6	Linear OOA(2¹⁹³, 32, F₂, 6, 167)	[i]
7	Linear OOA(2¹⁸⁷, 31, F₂, 6, 161)	[i]
8	Linear OOA(2¹⁸¹, 30, F₂, 6, 155)	[i]
9	Linear OOA(2²⁴², 41, F₂, 6, 212) (dual of [(41, 6), 4, 213]-NRT-code)	[i]	Juxtaposition for OOAs