MinT - Information on Result #1161652

Information on Result #1161652

Linear OOA(2²¹⁴, 31, F₂, 7, 197) (dual of [(31, 7), 3, 198]-NRT-code), using juxtaposition based on

linear OOA(2¹⁸, 3, F₂, 7, 18) (dual of [(3, 7), 3, 19]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(7;3,2) [i]
linear OOA(2¹⁹³, 28, F₂, 7, 178) (dual of [(28, 7), 3, 179]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(2¹⁸, 3, F₂, 7, 18) (dual of [(3, 7), 3, 19]-NRT-code) (see above)
  2. linear OOA(2¹⁷², 25, F₂, 7, 159) (dual of [(25, 7), 3, 160]-NRT-code), using
    - repeating each code word 5 times [i] based on linear OOA(2³², 5, F₂, 7, 31) (dual of [(5, 7), 3, 32]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(7;F,3P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, 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(2²¹⁴, 31, F₂, 7, 196) (dual of [(31, 7), 3, 197]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(2²¹⁴, 31, F₂, 7, 195) (dual of [(31, 7), 3, 196]-NRT-code)	[i]
3	Linear OOA(2²¹⁴, 31, F₂, 7, 194) (dual of [(31, 7), 3, 195]-NRT-code)	[i]
4	Linear OOA(2²¹⁴, 31, F₂, 7, 193) (dual of [(31, 7), 3, 194]-NRT-code)	[i]
5	Linear OOA(2²¹⁴, 31, F₂, 7, 192) (dual of [(31, 7), 3, 193]-NRT-code)	[i]
6	Linear OOA(2²¹⁴, 31, F₂, 7, 191) (dual of [(31, 7), 3, 192]-NRT-code)	[i]
7	Linear OOA(2²¹⁴, 31, F₂, 7, 190) (dual of [(31, 7), 3, 191]-NRT-code)	[i]
8	Linear OOA(2²¹⁴, 31, F₂, 7, 189) (dual of [(31, 7), 3, 190]-NRT-code)	[i]
9	Linear OOA(2²¹⁴, 31, F₂, 7, 188) (dual of [(31, 7), 3, 189]-NRT-code)	[i]
10	Linear OOA(2²¹⁴, 31, F₂, 7, 187) (dual of [(31, 7), 3, 188]-NRT-code)	[i]
11	Linear OOA(2²¹⁴, 31, F₂, 7, 186) (dual of [(31, 7), 3, 187]-NRT-code)	[i]
12	Linear OOA(2²¹⁴, 31, F₂, 7, 185) (dual of [(31, 7), 3, 186]-NRT-code)	[i]
13	Linear OOA(2²¹⁴, 31, F₂, 7, 184) (dual of [(31, 7), 3, 185]-NRT-code)	[i]
14	Linear OOA(2²¹⁴, 31, F₂, 7, 183) (dual of [(31, 7), 3, 184]-NRT-code)	[i]
15	Linear OOA(2²¹⁴, 31, F₂, 7, 182) (dual of [(31, 7), 3, 183]-NRT-code)	[i]
16	Linear OOA(2²¹⁴, 31, F₂, 7, 181) (dual of [(31, 7), 3, 182]-NRT-code)	[i]
17	Linear OOA(2²¹⁴, 31, F₂, 7, 180) (dual of [(31, 7), 3, 181]-NRT-code)	[i]
18	Linear OOA(2²¹⁴, 31, F₂, 7, 179) (dual of [(31, 7), 3, 180]-NRT-code)	[i]
19	Linear OOA(2²¹⁴, 31, F₂, 7, 178) (dual of [(31, 7), 3, 179]-NRT-code)	[i]
20	Linear OOA(2²¹³, 30, F₂, 7, 196)	[i]	Truncation for OOAs
21	Linear OOA(2²¹², 30, F₂, 7, 195)	[i]
22	Linear OOA(2²¹¹, 30, F₂, 7, 194)	[i]
23	Linear OOA(2²⁰⁶, 29, F₂, 7, 189)	[i]
24	Linear OOA(2²⁰⁵, 29, F₂, 7, 188)	[i]
25	Linear OOA(2²⁰⁴, 29, F₂, 7, 187)	[i]
26	Linear OOA(2²⁰¹, 29, F₂, 7, 184) (dual of [(29, 7), 2, 185]-NRT-code)	[i]
27	Linear OOA(2²⁰⁰, 29, F₂, 7, 183) (dual of [(29, 7), 3, 184]-NRT-code)	[i]
28	Linear OOA(2¹⁹⁹, 28, F₂, 7, 182)	[i]
29	Linear OOA(2¹⁹⁸, 28, F₂, 7, 181)	[i]
30	Linear OOA(2¹⁹⁷, 28, F₂, 7, 180)	[i]
31	Linear OOA(2¹⁹², 27, F₂, 7, 175)	[i]
32	Linear OOA(2¹⁹¹, 27, F₂, 7, 174)	[i]
33	Linear OOA(2¹⁹⁰, 27, F₂, 7, 173)	[i]
34	Linear OOA(2¹⁸⁵, 26, F₂, 7, 168)	[i]
35	Linear OOA(2¹⁸⁴, 26, F₂, 7, 167)	[i]
36	Linear OOA(2¹⁸³, 26, F₂, 7, 166)	[i]
37	Linear OOA(2¹⁷⁸, 25, F₂, 7, 161)	[i]
38	Linear OOA(2¹⁷⁷, 25, F₂, 7, 160)	[i]
39	Linear OOA(2¹⁷⁶, 25, F₂, 7, 159)	[i]
40	Linear OOA(2¹⁷³, 25, F₂, 7, 156) (dual of [(25, 7), 2, 157]-NRT-code)	[i]