MinT - Information on Result #1079596

Information on Result #1079596

Linear OOA(2¹⁴⁵, 2097155, F₂, 4, 12) (dual of [(2097155, 4), 8388475, 13]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁷, 5, F₂, 4, 6) (dual of [(5, 4), 13, 7]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(4;F,13P) [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(2¹³⁸, 2097150, F₂, 4, 12) (dual of [(2097150, 4), 8388462, 13]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2¹³⁸, 8388600, F₂, 12) (dual of [8388600, 8388462, 13]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹³⁸, large, F₂, 12) (dual of [large, large−138, 13]-code), using
    - the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(2²⁰⁹, 4194304, F₂, 4, 12) (dual of [(4194304, 4), 16777007, 13]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(2²¹⁰, 4194305, F₂, 4, 12) (dual of [(4194305, 4), 16777010, 13]-NRT-code)	[i]
3	Linear OOA(2²¹², 4194310, F₂, 4, 12) (dual of [(4194310, 4), 16777028, 13]-NRT-code)	[i]
4	Linear OOA(2²⁰⁹, 4194305, F₂, 4, 12) (dual of [(4194305, 4), 16777011, 13]-NRT-code)	[i]
5	Linear OOA(2¹⁴⁵, 2097155, F₂, 5, 12) (dual of [(2097155, 5), 10485630, 13]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
6	Linear OOA(2¹⁴⁵, 2097155, F₂, 6, 12) (dual of [(2097155, 6), 12582785, 13]-NRT-code)	[i]
7	Linear OOA(2¹⁴⁵, 2097155, F₂, 7, 12) (dual of [(2097155, 7), 14679940, 13]-NRT-code)	[i]
8	Linear OOA(2¹⁴⁵, 2097155, F₂, 8, 12) (dual of [(2097155, 8), 16777095, 13]-NRT-code)	[i]
9	Digital (133, 145, 2097155)-net over F₂	[i]