MinT - Information on Result #2955556

Information on Result #2955556

Linear OOA(2²⁵⁵, 37, F₂, 7, 227) (dual of [(37, 7), 4, 228]-NRT-code), using strength reduction based on linear OOA(2²⁵⁵, 37, F₂, 7, 228) (dual of [(37, 7), 4, 229]-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, using
    - an explicitly constructive algebraic function field [i]
2. linear OOA(2²²⁰, 32, F₂, 7, 197) (dual of [(32, 7), 4, 198]-NRT-code), using
  - juxtaposition [i] based on
    1. linear OOA(2³¹, 5, F₂, 7, 30) (dual of [(5, 7), 4, 31]-NRT-code) (see above)
    2. linear OOA(2¹⁸⁵, 27, F₂, 7, 166) (dual of [(27, 7), 4, 167]-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(2¹⁵⁰, 22, F₂, 7, 135) (dual of [(22, 7), 4, 136]-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(2¹¹⁵, 17, F₂, 7, 104) (dual of [(17, 7), 4, 105]-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(2⁸⁰, 12, F₂, 7, 73) (dual of [(12, 7), 4, 74]-NRT-code), using
        repeating each code word 2 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, 227)	[i]	OOA Duplication
2	Linear OOA(2²⁵⁴, 36, F₂, 7, 226)	[i]	Truncation for OOAs
3	Linear OOA(2²⁵³, 36, F₂, 7, 225)	[i]
4	Linear OOA(2²⁴⁷, 35, F₂, 7, 219)	[i]
5	Linear OOA(2²⁴⁶, 35, F₂, 7, 218)	[i]
6	Linear OOA(2²⁴³, 35, F₂, 7, 215) (dual of [(35, 7), 2, 216]-NRT-code)	[i]
7	Linear OOA(2²⁴⁰, 34, F₂, 7, 212)	[i]
8	Linear OOA(2²³⁹, 34, F₂, 7, 211)	[i]
9	Linear OOA(2²³⁵, 34, F₂, 7, 207) (dual of [(34, 7), 3, 208]-NRT-code)	[i]
10	Linear OOA(2²³⁴, 34, F₂, 7, 206) (dual of [(34, 7), 4, 207]-NRT-code)	[i]
11	Linear OOA(2²³³, 33, F₂, 7, 205)	[i]
12	Linear OOA(2²³², 33, F₂, 7, 204)	[i]
13	Linear OOA(2²²⁶, 32, F₂, 7, 198)	[i]
14	Linear OOA(2²²⁵, 32, F₂, 7, 197)	[i]