MinT - Information on Result #2993117

Information on Result #2993117

Linear OOA(2²⁶⁰, 33, F₂, 8, 234) (dual of [(33, 8), 4, 235]-NRT-code), using strength reduction based on linear OOA(2²⁶⁰, 33, F₂, 8, 235) (dual of [(33, 8), 4, 236]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(2²⁸, 4, F₂, 8, 27) (dual of [(4, 8), 4, 28]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(2²⁸, 5, F₂, 8, 27) (dual of [(5, 8), 12, 28]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(8;F,12P) [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(2²²⁸, 29, F₂, 8, 207) (dual of [(29, 8), 4, 208]-NRT-code), using
  - 8 step truncation [i] based on linear OOA(2²³⁶, 30, F₂, 8, 215) (dual of [(30, 8), 4, 216]-NRT-code), using
    - repeating each code word 6 times [i] based on linear OOA(2³⁶, 5, F₂, 8, 35) (dual of [(5, 8), 4, 36]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(8;F,4P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5 (see above)

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(2²⁵⁹, 32, F₂, 8, 233)	[i]	Truncation for OOAs
2	Linear OOA(2²⁵⁸, 32, F₂, 8, 232)	[i]
3	Linear OOA(2²⁵⁷, 32, F₂, 8, 231)	[i]
4	Linear OOA(2²⁵¹, 31, F₂, 8, 225)	[i]
5	Linear OOA(2²⁵⁰, 31, F₂, 8, 224)	[i]
6	Linear OOA(2²⁴⁹, 31, F₂, 8, 223)	[i]
7	Linear OOA(2²⁴³, 30, F₂, 8, 217)	[i]
8	Linear OOA(2²⁴², 30, F₂, 8, 216)	[i]
9	Linear OOA(2²⁴¹, 30, F₂, 8, 215)	[i]