MinT - Information on Result #894677

Information on Result #894677

Linear OOA(2¹²⁴, 65, F₂, 2, 64) (dual of [(65, 2), 6, 65]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁵⁹, 32, F₂, 2, 32) (dual of [(32, 2), 5, 33]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2²⁷, 16, F₂, 2, 16) (dual of [(16, 2), 5, 17]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(2¹¹, 8, F₂, 2, 8) (dual of [(8, 2), 5, 9]-NRT-code), using
        an explicit generator matrix by Edel [i]
      2. linear OOA(2¹⁶, 8, F₂, 2, 16) (dual of [(8, 2), 0, 17]-NRT-code), using
        complete OOA / dual of NRT-code with only one code word [i]
  2. linear OOA(2³², 16, F₂, 2, 32) (dual of [(16, 2), 0, 33]-NRT-code), using
    - complete OOA / dual of NRT-code with only one code word [i]
linear OOA(2⁶⁵, 33, F₂, 2, 64) (dual of [(33, 2), 1, 65]-NRT-code), using
- strength reduction [i] based on linear OOA(2⁶⁵, 33, F₂, 2, 65) (dual of [(33, 2), 1, 66]-NRT-code), using
  - dual of repetition NRT-code with length 33 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2²⁵³, 130, F₂, 2, 128) (dual of [(130, 2), 7, 129]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
2	Linear OOA(2²⁵³, 130, F₂, 2, 129) (dual of [(130, 2), 7, 130]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs