MinT - Information on Result #1079597

Information on Result #1079597

Linear OOA(2¹⁴⁶, 2097156, F₂, 4, 12) (dual of [(2097156, 4), 8388478, 13]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁸, 6, F₂, 4, 6) (dual of [(6, 4), 16, 7]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(4;F,17P) [i] based on function field F/F₂ with g(F) = 2 and N(F) ≥ 6, 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(2²¹³, 4194312, F₂, 4, 12) (dual of [(4194312, 4), 16777035, 13]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(2²¹⁰, 4194306, F₂, 4, 12) (dual of [(4194306, 4), 16777014, 13]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
3	Linear OOA(2¹⁴⁶, 2097156, F₂, 5, 12) (dual of [(2097156, 5), 10485634, 13]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
4	Linear OOA(2¹⁴⁶, 2097156, F₂, 6, 12) (dual of [(2097156, 6), 12582790, 13]-NRT-code)	[i]
5	Linear OOA(2¹⁴⁶, 2097156, F₂, 7, 12) (dual of [(2097156, 7), 14679946, 13]-NRT-code)	[i]
6	Linear OOA(2¹⁴⁶, 2097156, F₂, 8, 12) (dual of [(2097156, 8), 16777102, 13]-NRT-code)	[i]
7	Digital (134, 146, 2097156)-net over F₂	[i]