MinT - Information on Result #1025727

Information on Result #1025727

Linear OOA(2²²⁴, 76, F₂, 3, 166) (dual of [(76, 3), 4, 167]-NRT-code), using juxtaposition based on

linear OOA(2¹¹, 5, F₂, 3, 10) (dual of [(5, 3), 4, 11]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;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(2²⁰⁹, 71, F₂, 3, 155) (dual of [(71, 3), 4, 156]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(2¹¹, 5, F₂, 3, 10) (dual of [(5, 3), 4, 11]-NRT-code) (see above)
  2. linear OOA(2¹⁹⁴, 66, F₂, 3, 144) (dual of [(66, 3), 4, 145]-NRT-code), using
    - juxtaposition [i] based on
      1. linear OOA(2¹¹, 5, F₂, 3, 10) (dual of [(5, 3), 4, 11]-NRT-code) (see above)
      2. linear OOA(2¹⁷⁹, 61, F₂, 3, 133) (dual of [(61, 3), 4, 134]-NRT-code), using
        juxtaposition [i] based on
        linear OOA(2¹¹, 5, F₂, 3, 10) (dual of [(5, 3), 4, 11]-NRT-code) (see above)
        linear OOA(2¹⁶⁴, 56, F₂, 3, 122) (dual of [(56, 3), 4, 123]-NRT-code), using
        juxtaposition [i] based on
        linear OOA(2¹¹, 5, F₂, 3, 10) (dual of [(5, 3), 4, 11]-NRT-code) (see above)
        linear OOA(2¹⁴⁹, 51, F₂, 3, 111) (dual of [(51, 3), 4, 112]-NRT-code), using
        juxtaposition [i] based on
        linear OOA(2¹¹, 5, F₂, 3, 10) (dual of [(5, 3), 4, 11]-NRT-code) (see above)
        linear OOA(2¹³⁴, 46, F₂, 3, 100) (dual of [(46, 3), 4, 101]-NRT-code), using
        juxtaposition [i] based on
        linear OOA(2¹¹, 5, F₂, 3, 10) (dual of [(5, 3), 4, 11]-NRT-code) (see above)
        linear OOA(2¹¹⁹, 41, F₂, 3, 89) (dual of [(41, 3), 4, 90]-NRT-code), using
        juxtaposition [i] based on
        linear OOA(2¹¹, 5, F₂, 3, 10) (dual of [(5, 3), 4, 11]-NRT-code) (see above)
        linear OOA(2¹⁰⁴, 36, F₂, 3, 78) (dual of [(36, 3), 4, 79]-NRT-code), using
        juxtaposition [i] based on
        linear OOA(2¹¹, 5, F₂, 3, 10) (dual of [(5, 3), 4, 11]-NRT-code) (see above)
        linear OOA(2⁸⁹, 31, F₂, 3, 67) (dual of [(31, 3), 4, 68]-NRT-code), using
        juxtaposition [i] based on
        linear OOA(2¹¹, 5, F₂, 3, 10) (dual of [(5, 3), 4, 11]-NRT-code) (see above)
        linear OOA(2⁷⁴, 26, F₂, 3, 56) (dual of [(26, 3), 4, 57]-NRT-code), using
        juxtaposition [i] based on
        linear OOA(2¹¹, 5, F₂, 3, 10) (dual of [(5, 3), 4, 11]-NRT-code) (see above)
        linear OOA(2⁵⁹, 21, F₂, 3, 45) (dual of [(21, 3), 4, 46]-NRT-code), using
        juxtaposition [i] based on
        linear OOA(2¹¹, 5, F₂, 3, 10) (dual of [(5, 3), 4, 11]-NRT-code) (see above)
        linear OOA(2⁴⁴, 16, F₂, 3, 34) (dual of [(16, 3), 4, 35]-NRT-code), using
        juxtaposition [i] based on
        linear OOA(2¹¹, 5, F₂, 3, 10) (dual of [(5, 3), 4, 11]-NRT-code) (see above)
        linear OOA(2²⁹, 11, F₂, 3, 23) (dual of [(11, 3), 4, 24]-NRT-code), using
        juxtaposition [i] based on
        linear OOA(2¹¹, 5, F₂, 3, 10) (dual of [(5, 3), 4, 11]-NRT-code) (see above)
        linear OOA(2¹⁴, 6, F₂, 3, 12) (dual of [(6, 3), 4, 13]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(3;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(2²²⁴, 76, F₂, 3, 165) (dual of [(76, 3), 4, 166]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(2²²⁴, 76, F₂, 3, 164) (dual of [(76, 3), 4, 165]-NRT-code)	[i]
3	Linear OOA(2²²⁴, 76, F₂, 3, 163) (dual of [(76, 3), 4, 164]-NRT-code)	[i]
4	Linear OOA(2²²⁴, 76, F₂, 3, 162) (dual of [(76, 3), 4, 163]-NRT-code)	[i]
5	Linear OOA(2²²⁴, 76, F₂, 3, 161) (dual of [(76, 3), 4, 162]-NRT-code)	[i]
6	Linear OOA(2²²⁴, 76, F₂, 3, 160) (dual of [(76, 3), 4, 161]-NRT-code)	[i]
7	Linear OOA(2²²⁴, 76, F₂, 3, 159) (dual of [(76, 3), 4, 160]-NRT-code)	[i]
8	Linear OOA(2²²⁴, 76, F₂, 3, 158) (dual of [(76, 3), 4, 159]-NRT-code)	[i]
9	Linear OOA(2²²⁴, 76, F₂, 3, 157) (dual of [(76, 3), 4, 158]-NRT-code)	[i]
10	Linear OOA(2²¹⁹, 74, F₂, 3, 161) (dual of [(74, 3), 3, 162]-NRT-code)	[i]	Truncation for OOAs
11	Linear OOA(2²¹⁸, 74, F₂, 3, 160) (dual of [(74, 3), 4, 161]-NRT-code)	[i]
12	Linear OOA(2²¹⁷, 73, F₂, 3, 159) (dual of [(73, 3), 2, 160]-NRT-code)	[i]
13	Linear OOA(2²¹¹, 71, F₂, 3, 153) (dual of [(71, 3), 2, 154]-NRT-code)	[i]
14	Linear OOA(2²³⁹, 81, F₂, 3, 177) (dual of [(81, 3), 4, 178]-NRT-code)	[i]	Juxtaposition for OOAs
15	Linear OOA(2²²⁴, 38, F₂, 6, 166) (dual of [(38, 6), 4, 167]-NRT-code)	[i]	OOA Folding