MinT - Information on Result #2781405

Information on Result #2781405

Linear OOA(2¹⁷², 44, F₂, 4, 137) (dual of [(44, 4), 4, 138]-NRT-code), using 12 step truncation based on linear OOA(2¹⁸⁴, 47, F₂, 4, 149) (dual of [(47, 4), 4, 150]-NRT-code), using

juxtaposition [i] based on
1. 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]
2. linear OOA(2¹⁶⁴, 42, F₂, 4, 133) (dual of [(42, 4), 4, 134]-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(2¹⁴⁴, 37, F₂, 4, 117) (dual of [(37, 4), 4, 118]-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(2¹²⁴, 32, F₂, 4, 101) (dual of [(32, 4), 4, 102]-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(2¹⁰⁴, 27, F₂, 4, 85) (dual of [(27, 4), 4, 86]-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(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		This result only	Method
1	Linear OOA(2¹⁷², 22, F₂, 8, 137) (dual of [(22, 8), 4, 138]-NRT-code)	[i]		OOA Folding