MinT - Information on Result #1161649

Information on Result #1161649

Linear OOA(2¹⁷⁹, 26, F₂, 7, 165) (dual of [(26, 7), 3, 166]-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(2¹⁵⁸, 23, F₂, 7, 146) (dual of [(23, 7), 3, 147]-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(2¹³⁷, 20, F₂, 7, 127) (dual of [(20, 7), 3, 128]-NRT-code), using
    - repeating each code word 4 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(2¹⁷⁹, 26, F₂, 7, 164) (dual of [(26, 7), 3, 165]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(2¹⁷⁹, 26, F₂, 7, 163) (dual of [(26, 7), 3, 164]-NRT-code)	[i]
3	Linear OOA(2¹⁷⁹, 26, F₂, 7, 162) (dual of [(26, 7), 3, 163]-NRT-code)	[i]
4	Linear OOA(2¹⁷⁹, 26, F₂, 7, 161) (dual of [(26, 7), 3, 162]-NRT-code)	[i]
5	Linear OOA(2¹⁷⁹, 26, F₂, 7, 160) (dual of [(26, 7), 3, 161]-NRT-code)	[i]
6	Linear OOA(2¹⁷⁹, 26, F₂, 7, 159) (dual of [(26, 7), 3, 160]-NRT-code)	[i]
7	Linear OOA(2¹⁷⁹, 26, F₂, 7, 158) (dual of [(26, 7), 3, 159]-NRT-code)	[i]
8	Linear OOA(2¹⁷⁹, 26, F₂, 7, 157) (dual of [(26, 7), 3, 158]-NRT-code)	[i]
9	Linear OOA(2¹⁷⁹, 26, F₂, 7, 156) (dual of [(26, 7), 3, 157]-NRT-code)	[i]
10	Linear OOA(2¹⁷⁸, 25, F₂, 7, 164)	[i]	Truncation for OOAs
11	Linear OOA(2¹⁷⁷, 25, F₂, 7, 163)	[i]
12	Linear OOA(2¹⁷⁶, 25, F₂, 7, 162)	[i]
13	Linear OOA(2¹⁷³, 25, F₂, 7, 159) (dual of [(25, 7), 2, 160]-NRT-code)	[i]
14	Linear OOA(2¹⁷¹, 24, F₂, 7, 157)	[i]
15	Linear OOA(2¹⁷⁰, 24, F₂, 7, 156)	[i]
16	Linear OOA(2¹⁶⁹, 24, F₂, 7, 155)	[i]
17	Linear OOA(2¹⁶⁴, 23, F₂, 7, 150)	[i]
18	Linear OOA(2¹⁶³, 23, F₂, 7, 149)	[i]
19	Linear OOA(2¹⁶², 23, F₂, 7, 148)	[i]
20	Linear OOA(2¹⁵⁹, 23, F₂, 7, 145) (dual of [(23, 7), 2, 146]-NRT-code)	[i]
21	Linear OOA(2¹⁵⁷, 22, F₂, 7, 143)	[i]
22	Linear OOA(2¹⁵⁶, 22, F₂, 7, 142)	[i]
23	Linear OOA(2¹⁵⁵, 22, F₂, 7, 141)	[i]
24	Linear OOA(2¹⁵⁰, 21, F₂, 7, 136)	[i]
25	Linear OOA(2¹⁴⁹, 21, F₂, 7, 135)	[i]
26	Linear OOA(2¹⁴⁸, 21, F₂, 7, 134)	[i]