MinT - Information on Result #2955641

Information on Result #2955641

Linear OOA(2²⁵⁶, 37, F₂, 7, 233) (dual of [(37, 7), 3, 234]-NRT-code), using strength reduction based on linear OOA(2²⁵⁶, 37, F₂, 7, 235) (dual of [(37, 7), 3, 236]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(2¹⁸, 3, F₂, 7, 18) (dual of [(3, 7), 3, 19]-NRT-code), using
  - extended Reedâ€“Solomon NRT-code RS_e(7;3,2) [i]
2. linear OOA(2²³⁵, 34, F₂, 7, 216) (dual of [(34, 7), 3, 217]-NRT-code), using
  - 7 step truncation [i] based on linear OOA(2²⁴², 35, F₂, 7, 223) (dual of [(35, 7), 3, 224]-NRT-code), using
    - repeating each code word 7 times [i] based on linear OOA(2³², 5, F₂, 7, 31) (dual of [(5, 7), 3, 32]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(7;F,3P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, 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, 233)	[i]	OOA Duplication
2	Linear OOA(2²⁵⁵, 36, F₂, 7, 232)	[i]	Truncation for OOAs
3	Linear OOA(2²⁵⁴, 36, F₂, 7, 231)	[i]
4	Linear OOA(2²⁵³, 36, F₂, 7, 230)	[i]
5	Linear OOA(2²⁴⁸, 35, F₂, 7, 225)	[i]
6	Linear OOA(2²⁴⁷, 35, F₂, 7, 224)	[i]
7	Linear OOA(2²⁴⁶, 35, F₂, 7, 223)	[i]
8	Linear OOA(2²⁴³, 35, F₂, 7, 220) (dual of [(35, 7), 2, 221]-NRT-code)	[i]
9	Linear OOA(2²⁴¹, 34, F₂, 7, 218)	[i]
10	Linear OOA(2²⁴⁰, 34, F₂, 7, 217)	[i]
11	Linear OOA(2²³⁹, 34, F₂, 7, 216)	[i]
12	Linear OOA(2²³⁵, 34, F₂, 7, 212) (dual of [(34, 7), 3, 213]-NRT-code)	[i]
13	Linear OOA(2²³⁴, 33, F₂, 7, 211)	[i]
14	Linear OOA(2²³³, 33, F₂, 7, 210)	[i]
15	Linear OOA(2²³², 33, F₂, 7, 209)	[i]
16	Linear OOA(2²²⁷, 32, F₂, 7, 204)	[i]
17	Linear OOA(2²²⁶, 32, F₂, 7, 203)	[i]
18	Linear OOA(2²²⁵, 32, F₂, 7, 202)	[i]