MinT - Information on Result #2766165

Information on Result #2766165

Linear OOA(2²²⁸, 58, F₂, 4, 179) (dual of [(58, 4), 4, 180]-NRT-code), using strength reduction based on linear OOA(2²²⁸, 58, F₂, 4, 184) (dual of [(58, 4), 4, 185]-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(2²⁰⁸, 53, F₂, 4, 168) (dual of [(53, 4), 4, 169]-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(2¹⁸⁸, 48, F₂, 4, 152) (dual of [(48, 4), 4, 153]-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(2¹⁶⁸, 43, F₂, 4, 136) (dual of [(43, 4), 4, 137]-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(2¹⁴⁸, 38, F₂, 4, 120) (dual of [(38, 4), 4, 121]-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(2¹²⁸, 33, F₂, 4, 104) (dual of [(33, 4), 4, 105]-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(2¹⁰⁸, 28, F₂, 4, 88) (dual of [(28, 4), 4, 89]-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(2⁸⁸, 23, F₂, 4, 72) (dual of [(23, 4), 4, 73]-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(2⁶⁸, 18, F₂, 4, 56) (dual of [(18, 4), 4, 57]-NRT-code), using
        repeating each code word 3 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(2²²⁸, 29, F₂, 8, 179) (dual of [(29, 8), 4, 180]-NRT-code)	[i]		OOA Folding