MinT - Information on Result #1087049

Information on Result #1087049

Linear OOA(2¹⁴⁴, 37, F₂, 4, 117) (dual of [(37, 4), 4, 118]-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(2¹²⁴, 32, F₂, 4, 101) (dual of [(32, 4), 4, 102]-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(2¹⁰⁴, 27, F₂, 4, 85) (dual of [(27, 4), 4, 86]-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(2⁸⁴, 22, F₂, 4, 69) (dual of [(22, 4), 4, 70]-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(2⁶⁴, 17, F₂, 4, 53) (dual of [(17, 4), 4, 54]-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(2⁴⁴, 12, F₂, 4, 37) (dual of [(12, 4), 4, 38]-NRT-code), using
        repeating each code word 2 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(2¹⁴⁴, 37, F₂, 4, 116) (dual of [(37, 4), 4, 117]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(2¹⁴⁴, 37, F₂, 4, 115) (dual of [(37, 4), 4, 116]-NRT-code)	[i]
3	Linear OOA(2¹⁴⁴, 37, F₂, 4, 114) (dual of [(37, 4), 4, 115]-NRT-code)	[i]
4	Linear OOA(2¹⁴⁴, 37, F₂, 4, 113) (dual of [(37, 4), 4, 114]-NRT-code)	[i]
5	Linear OOA(2¹⁴⁴, 37, F₂, 4, 112) (dual of [(37, 4), 4, 113]-NRT-code)	[i]
6	Linear OOA(2¹⁴⁴, 37, F₂, 4, 111) (dual of [(37, 4), 4, 112]-NRT-code)	[i]
7	Linear OOA(2¹⁴⁴, 37, F₂, 4, 110) (dual of [(37, 4), 4, 111]-NRT-code)	[i]
8	Linear OOA(2¹⁴⁴, 37, F₂, 4, 109) (dual of [(37, 4), 4, 110]-NRT-code)	[i]
9	Linear OOA(2¹⁴⁴, 37, F₂, 4, 108) (dual of [(37, 4), 4, 109]-NRT-code)	[i]
10	Linear OOA(2¹⁴⁴, 37, F₂, 4, 107) (dual of [(37, 4), 4, 108]-NRT-code)	[i]
11	Linear OOA(2¹⁴⁴, 37, F₂, 4, 106) (dual of [(37, 4), 4, 107]-NRT-code)	[i]
12	Linear OOA(2¹⁴⁴, 37, F₂, 4, 105) (dual of [(37, 4), 4, 106]-NRT-code)	[i]
13	Linear OOA(2¹⁴⁴, 37, F₂, 4, 104) (dual of [(37, 4), 4, 105]-NRT-code)	[i]
14	Linear OOA(2¹³³, 34, F₂, 4, 106) (dual of [(34, 4), 3, 107]-NRT-code)	[i]	Truncation for OOAs
15	Linear OOA(2¹³², 34, F₂, 4, 105) (dual of [(34, 4), 4, 106]-NRT-code)	[i]	Truncation for OOAs
16	Linear OOA(2¹⁶⁴, 42, F₂, 4, 133) (dual of [(42, 4), 4, 134]-NRT-code)	[i]	Juxtaposition for OOAs