MinT - Information on Result #2955558

Information on Result #2955558

Linear OOA(2²⁵⁵, 37, F₂, 7, 224) (dual of [(37, 7), 4, 225]-NRT-code), using strength reduction based on linear OOA(2²⁵⁵, 37, F₂, 7, 226) (dual of [(37, 7), 4, 227]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(2²⁴, 4, F₂, 7, 23) (dual of [(4, 7), 4, 24]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(2²⁴, 5, F₂, 7, 23) (dual of [(5, 7), 11, 24]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(7;F,11P) [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(2²²⁷, 33, F₂, 7, 202) (dual of [(33, 7), 4, 203]-NRT-code), using
  - strength reduction [i] based on linear OOA(2²²⁷, 33, F₂, 7, 203) (dual of [(33, 7), 4, 204]-NRT-code), using
    - juxtaposition [i] based on
      1. linear OOA(2³¹, 5, F₂, 7, 30) (dual of [(5, 7), 4, 31]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(7;F,4P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5 (see above)
      2. linear OOA(2¹⁹², 28, F₂, 7, 172) (dual of [(28, 7), 4, 173]-NRT-code), using
        juxtaposition [i] based on
        linear OOA(2³¹, 5, F₂, 7, 30) (dual of [(5, 7), 4, 31]-NRT-code) (see above)
        linear OOA(2¹⁵⁷, 23, F₂, 7, 141) (dual of [(23, 7), 4, 142]-NRT-code), using
        juxtaposition [i] based on
        linear OOA(2³¹, 5, F₂, 7, 30) (dual of [(5, 7), 4, 31]-NRT-code) (see above)
        linear OOA(2¹²², 18, F₂, 7, 110) (dual of [(18, 7), 4, 111]-NRT-code), using
        repeating each code word 3 times [i] based on linear OOA(2³⁸, 6, F₂, 7, 36) (dual of [(6, 7), 4, 37]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(7;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(2²⁶⁰, 37, F₂, 7, 224)	[i]	OOA Duplication
2	Linear OOA(2²⁵⁴, 36, F₂, 7, 223)	[i]	Truncation for OOAs
3	Linear OOA(2²⁵³, 36, F₂, 7, 222)	[i]
4	Linear OOA(2²⁴⁷, 35, F₂, 7, 216)	[i]
5	Linear OOA(2²⁴⁶, 35, F₂, 7, 215)	[i]
6	Linear OOA(2²⁴³, 35, F₂, 7, 212) (dual of [(35, 7), 2, 213]-NRT-code)	[i]