MinT - Information on Result #1146239

Information on Result #1146239

Linear OOA(2²¹⁸, 37, F₂, 6, 191) (dual of [(37, 6), 4, 192]-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(2¹⁸⁸, 32, F₂, 6, 165) (dual of [(32, 6), 4, 166]-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(2¹⁵⁸, 27, F₂, 6, 139) (dual of [(27, 6), 4, 140]-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(2¹²⁸, 22, F₂, 6, 113) (dual of [(22, 6), 4, 114]-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(2⁹⁸, 17, F₂, 6, 87) (dual of [(17, 6), 4, 88]-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(2⁶⁸, 12, F₂, 6, 61) (dual of [(12, 6), 4, 62]-NRT-code), using
        repeating each code word 2 times [i] based on 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(2²¹⁸, 37, F₂, 6, 190) (dual of [(37, 6), 4, 191]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(2²¹⁸, 37, F₂, 6, 189) (dual of [(37, 6), 4, 190]-NRT-code)	[i]
3	Linear OOA(2²¹⁸, 37, F₂, 6, 188) (dual of [(37, 6), 4, 189]-NRT-code)	[i]
4	Linear OOA(2²¹⁸, 37, F₂, 6, 187) (dual of [(37, 6), 4, 188]-NRT-code)	[i]
5	Linear OOA(2²¹⁸, 37, F₂, 6, 186) (dual of [(37, 6), 4, 187]-NRT-code)	[i]
6	Linear OOA(2²¹⁸, 37, F₂, 6, 185) (dual of [(37, 6), 4, 186]-NRT-code)	[i]
7	Linear OOA(2²¹⁸, 37, F₂, 6, 184) (dual of [(37, 6), 4, 185]-NRT-code)	[i]
8	Linear OOA(2²¹⁸, 37, F₂, 6, 183) (dual of [(37, 6), 4, 184]-NRT-code)	[i]
9	Linear OOA(2²¹⁸, 37, F₂, 6, 182) (dual of [(37, 6), 4, 183]-NRT-code)	[i]
10	Linear OOA(2²¹⁸, 37, F₂, 6, 181) (dual of [(37, 6), 4, 182]-NRT-code)	[i]
11	Linear OOA(2²¹⁸, 37, F₂, 6, 180) (dual of [(37, 6), 4, 181]-NRT-code)	[i]
12	Linear OOA(2²¹⁸, 37, F₂, 6, 179) (dual of [(37, 6), 4, 180]-NRT-code)	[i]
13	Linear OOA(2²¹⁸, 37, F₂, 6, 178) (dual of [(37, 6), 4, 179]-NRT-code)	[i]
14	Linear OOA(2²¹⁸, 37, F₂, 6, 177) (dual of [(37, 6), 4, 178]-NRT-code)	[i]
15	Linear OOA(2²¹⁸, 37, F₂, 6, 176) (dual of [(37, 6), 4, 177]-NRT-code)	[i]
16	Linear OOA(2²¹⁸, 37, F₂, 6, 175) (dual of [(37, 6), 4, 176]-NRT-code)	[i]
17	Linear OOA(2²¹⁸, 37, F₂, 6, 174) (dual of [(37, 6), 4, 175]-NRT-code)	[i]
18	Linear OOA(2²¹⁷, 36, F₂, 6, 190)	[i]	Truncation for OOAs
19	Linear OOA(2²¹¹, 35, F₂, 6, 184)	[i]
20	Linear OOA(2²⁰⁵, 34, F₂, 6, 178)	[i]
21	Linear OOA(2²⁰¹, 34, F₂, 6, 174) (dual of [(34, 6), 3, 175]-NRT-code)	[i]
22	Linear OOA(2²⁰⁰, 34, F₂, 6, 173) (dual of [(34, 6), 4, 174]-NRT-code)	[i]
23	Linear OOA(2¹⁹⁹, 33, F₂, 6, 172)	[i]
24	Linear OOA(2¹⁹³, 32, F₂, 6, 166)	[i]
25	Linear OOA(2¹⁸⁷, 31, F₂, 6, 160)	[i]
26	Linear OOA(2²⁴⁸, 42, F₂, 6, 217) (dual of [(42, 6), 4, 218]-NRT-code)	[i]	Juxtaposition for OOAs