MinT - Information on Result #2613306

Information on Result #2613306

Linear OOA(2¹⁵², 52, F₂, 3, 112) (dual of [(52, 3), 4, 113]-NRT-code), using strength reduction based on linear OOA(2¹⁵², 52, F₂, 3, 113) (dual of [(52, 3), 4, 114]-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(2¹³⁷, 47, F₂, 3, 102) (dual of [(47, 3), 4, 103]-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(2¹²², 42, F₂, 3, 91) (dual of [(42, 3), 4, 92]-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(2¹⁰⁷, 37, F₂, 3, 80) (dual of [(37, 3), 4, 81]-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(2⁹², 32, F₂, 3, 69) (dual of [(32, 3), 4, 70]-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(2⁷⁷, 27, F₂, 3, 58) (dual of [(27, 3), 4, 59]-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(2⁶², 22, F₂, 3, 47) (dual of [(22, 3), 4, 48]-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(2⁴⁷, 17, F₂, 3, 36) (dual of [(17, 3), 4, 37]-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(2³², 12, F₂, 3, 25) (dual of [(12, 3), 4, 26]-NRT-code), using
        repeating each code word 2 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(2¹⁵², 26, F₂, 6, 112) (dual of [(26, 6), 4, 113]-NRT-code)	[i]		OOA Folding