MinT - Information on Result #908605

Information on Result #908605

Linear OOA(2¹⁵⁷, 82, F₂, 2, 82) (dual of [(82, 2), 7, 83]-NRT-code), using juxtaposition based on

linear OOA(2¹⁷, 12, F₂, 2, 10) (dual of [(12, 2), 7, 11]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2¹⁷, 13, F₂, 2, 10) (dual of [(13, 2), 9, 11]-NRT-code), using
  - extracting embedded OOA [i] based on digital (7, 17, 13)-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(2¹⁸⁹, 98, F₂, 2, 98) (dual of [(98, 2), 7, 99]-NRT-code)	[i]		Juxtaposition for OOAs