MinT - Information on Result #1087062

Information on Result #1087062

Linear OOA(2²²⁸, 58, F₂, 4, 184) (dual of [(58, 4), 4, 185]-NRT-code), using juxtaposition based on

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]
linear OOA(2²⁰⁸, 53, F₂, 4, 168) (dual of [(53, 4), 4, 169]-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(2¹⁸⁸, 48, F₂, 4, 152) (dual of [(48, 4), 4, 153]-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(2¹⁶⁸, 43, F₂, 4, 136) (dual of [(43, 4), 4, 137]-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(2¹⁴⁸, 38, F₂, 4, 120) (dual of [(38, 4), 4, 121]-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(2¹²⁸, 33, F₂, 4, 104) (dual of [(33, 4), 4, 105]-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(2¹⁰⁸, 28, F₂, 4, 88) (dual of [(28, 4), 4, 89]-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(2⁸⁸, 23, F₂, 4, 72) (dual of [(23, 4), 4, 73]-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(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		Method
1	Linear OOA(2²²⁸, 58, F₂, 4, 183) (dual of [(58, 4), 4, 184]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(2²²⁸, 58, F₂, 4, 182) (dual of [(58, 4), 4, 183]-NRT-code)	[i]
3	Linear OOA(2²²⁸, 58, F₂, 4, 181) (dual of [(58, 4), 4, 182]-NRT-code)	[i]
4	Linear OOA(2²²⁸, 58, F₂, 4, 180) (dual of [(58, 4), 4, 181]-NRT-code)	[i]
5	Linear OOA(2²²⁸, 58, F₂, 4, 179) (dual of [(58, 4), 4, 180]-NRT-code)	[i]
6	Linear OOA(2²²⁸, 58, F₂, 4, 178) (dual of [(58, 4), 4, 179]-NRT-code)	[i]
7	Linear OOA(2²²⁸, 58, F₂, 4, 177) (dual of [(58, 4), 4, 178]-NRT-code)	[i]
8	Linear OOA(2²²⁸, 58, F₂, 4, 176) (dual of [(58, 4), 4, 177]-NRT-code)	[i]
9	Linear OOA(2²²⁸, 58, F₂, 4, 175) (dual of [(58, 4), 4, 176]-NRT-code)	[i]
10	Linear OOA(2²²⁸, 58, F₂, 4, 174) (dual of [(58, 4), 4, 175]-NRT-code)	[i]
11	Linear OOA(2²²⁸, 58, F₂, 4, 173) (dual of [(58, 4), 4, 174]-NRT-code)	[i]
12	Linear OOA(2²²⁸, 58, F₂, 4, 172) (dual of [(58, 4), 4, 173]-NRT-code)	[i]
13	Linear OOA(2²¹², 54, F₂, 4, 168) (dual of [(54, 4), 4, 169]-NRT-code)	[i]	Truncation for OOAs
14	Linear OOA(2¹⁹³, 49, F₂, 4, 149) (dual of [(49, 4), 3, 150]-NRT-code)	[i]
15	Linear OOA(2¹⁹², 49, F₂, 4, 148) (dual of [(49, 4), 4, 149]-NRT-code)	[i]
16	Linear OOA(2²⁴⁸, 63, F₂, 4, 200) (dual of [(63, 4), 4, 201]-NRT-code)	[i]	Juxtaposition for OOAs
17	Linear OOA(2²²⁸, 29, F₂, 8, 184) (dual of [(29, 8), 4, 185]-NRT-code)	[i]	OOA Folding