MinT - Information on Result #908602

Information on Result #908602

Linear OOA(2¹⁵⁵, 81, F₂, 2, 81) (dual of [(81, 2), 7, 82]-NRT-code), using juxtaposition based on

linear OOA(2¹⁵, 11, F₂, 2, 9) (dual of [(11, 2), 7, 10]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2¹⁵, 12, F₂, 2, 9) (dual of [(12, 2), 9, 10]-NRT-code), using
  - extracting embedded OOA [i] based on digital (6, 15, 12)-net over F₂, using
    - linear code embedding found in a computer search [i]
linear OOA(2¹³³, 70, F₂, 2, 71) (dual of [(70, 2), 7, 72]-NRT-code), using
- repeating each code word 2 times [i] based on linear OOA(2⁶³, 35, F₂, 2, 35) (dual of [(35, 2), 7, 36]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(2²⁸, 17, F₂, 2, 17) (dual of [(17, 2), 6, 18]-NRT-code), using
      - (u,Â u+v)-construction [i] based on
        linear OOA(2¹¹, 8, F₂, 2, 8) (dual of [(8, 2), 5, 9]-NRT-code), using
        an explicit generator matrix by Edel [i]
        linear OOA(2¹⁷, 9, F₂, 2, 17) (dual of [(9, 2), 1, 18]-NRT-code), using
        dual of repetition NRT-code with length 9 [i]
    2. linear OOA(2³⁵, 18, F₂, 2, 35) (dual of [(18, 2), 1, 36]-NRT-code), using
      - dual of repetition NRT-code with length 18 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2¹⁸⁷, 97, F₂, 2, 97) (dual of [(97, 2), 7, 98]-NRT-code)	[i]		Juxtaposition for OOAs