MinT - Information on Result #1079511

Information on Result #1079511

Linear OOA(2¹²², 2097155, F₂, 4, 11) (dual of [(2097155, 4), 8388498, 12]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁶, 5, F₂, 4, 5) (dual of [(5, 4), 14, 6]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(4;F,14P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, using
  - an explicitly constructive algebraic function field [i]
linear OOA(2¹¹⁶, 2097150, F₂, 4, 11) (dual of [(2097150, 4), 8388484, 12]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2¹¹⁶, 8388600, F₂, 11) (dual of [8388600, 8388484, 12]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹¹⁶, large, F₂, 11) (dual of [large, large−116, 12]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [0,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(2¹⁶⁶, 4194308, F₂, 4, 11) (dual of [(4194308, 4), 16777066, 12]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(2¹⁶⁸, 4194310, F₂, 4, 11) (dual of [(4194310, 4), 16777072, 12]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
3	Linear OOA(2¹²², 2097155, F₂, 5, 11) (dual of [(2097155, 5), 10485653, 12]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
4	Linear OOA(2¹²², 2097155, F₂, 6, 11) (dual of [(2097155, 6), 12582808, 12]-NRT-code)	[i]
5	Linear OOA(2¹²², 2097155, F₂, 7, 11) (dual of [(2097155, 7), 14679963, 12]-NRT-code)	[i]
6	Linear OOA(2¹²², 2097155, F₂, 8, 11) (dual of [(2097155, 8), 16777118, 12]-NRT-code)	[i]
7	Digital (111, 122, 2097155)-net over F₂	[i]