MinT - Information on Result #2653112

Information on Result #2653112

Linear OOA(2¹⁵⁸, 54, F₂, 3, 114) (dual of [(54, 3), 4, 115]-NRT-code), using 12 step truncation based on linear OOA(2¹⁷⁰, 58, F₂, 3, 126) (dual of [(58, 3), 4, 127]-NRT-code), using

juxtaposition [i] based on
1. 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]
2. linear OOA(2¹⁵⁵, 53, F₂, 3, 115) (dual of [(53, 3), 4, 116]-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(2¹⁴⁰, 48, F₂, 3, 104) (dual of [(48, 3), 4, 105]-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(2¹²⁵, 43, F₂, 3, 93) (dual of [(43, 3), 4, 94]-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(2¹¹⁰, 38, F₂, 3, 82) (dual of [(38, 3), 4, 83]-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(2⁹⁵, 33, F₂, 3, 71) (dual of [(33, 3), 4, 72]-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(2⁸⁰, 28, F₂, 3, 60) (dual of [(28, 3), 4, 61]-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(2⁶⁵, 23, F₂, 3, 49) (dual of [(23, 3), 4, 50]-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(2⁵⁰, 18, F₂, 3, 38) (dual of [(18, 3), 4, 39]-NRT-code), using
        repeating each code word 3 times [i] based on 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		This result only	Method
1	Linear OOA(2¹⁵⁸, 27, F₂, 6, 114) (dual of [(27, 6), 4, 115]-NRT-code)	[i]		OOA Folding