MinT - Information on Result #911385

Information on Result #911385

Linear OOA(2⁸¹, 45, F₂, 2, 48) (dual of [(45, 2), 9, 49]-NRT-code), using concatenation of two NRT-codes based on

linear OA(8⁶, 9, F₈, 6) (dual of [9, 3, 7]-code or 9-arc in PG(5,8)), using
- extended Reedâ€“Solomon code RS_e(3,8) [i]
linear OOA(2⁷, 5, F₂, 2, 6) (dual of [(5, 2), 3, 7]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;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		This result only	Method
1	Linear OOA(2⁸³, 46, F₂, 2, 48) (dual of [(46, 2), 9, 49]-NRT-code)	[i]		NRT-Code Embedding in Larger Space
2	Linear OOA(2⁸⁰, 44, F₂, 2, 47) (dual of [(44, 2), 8, 48]-NRT-code)	[i]		Truncation for OOAs
3	Linear OOA(2⁷⁹, 44, F₂, 2, 46) (dual of [(44, 2), 9, 47]-NRT-code)	[i]
4	Linear OOA(2⁷⁸, 43, F₂, 2, 45) (dual of [(43, 2), 8, 46]-NRT-code)	[i]
5	Linear OOA(2⁷⁷, 43, F₂, 2, 44) (dual of [(43, 2), 9, 45]-NRT-code)	[i]
6	Linear OOA(2¹⁰¹, 55, F₂, 2, 56) (dual of [(55, 2), 9, 57]-NRT-code)	[i]		Juxtaposition for OOAs
7	Linear OOA(2⁸¹, 22, F₂, 4, 48) (dual of [(22, 4), 7, 49]-NRT-code)	[i]		OOA Folding