MinT - Information on Result #906621

Information on Result #906621

Linear OOA(7⁶², 44, F₇, 2, 35) (dual of [(44, 2), 26, 36]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(7⁹, 11, F₇, 2, 8) (dual of [(11, 2), 13, 9]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(7⁹, 13, F₇, 2, 8) (dual of [(13, 2), 17, 9]-NRT-code), using
  - extracting embedded OOA [i] based on digital (1, 9, 13)-net over F₇, using
    - 4 times m-reduction [i] based on digital (1, 13, 13)-net over F₇, using
      - a shift-net [i]
linear OOA(7¹², 11, F₇, 2, 11) (dual of [(11, 2), 10, 12]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(7¹², 13, F₇, 2, 11) (dual of [(13, 2), 14, 12]-NRT-code), using
  - extracting embedded OOA [i] based on digital (1, 12, 13)-net over F₇, using
    - 1 times m-reduction [i] based on digital (1, 13, 13)-net over F₇ (see above)
linear OOA(7¹⁹, 11, F₇, 2, 17) (dual of [(11, 2), 3, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(7¹⁹, 22, F₇, 17) (dual of [22, 3, 18]-code), using
  - a projective code based on a Barlotti arc [i]
linear OOA(7²², 11, F₇, 2, 22) (dual of [(11, 2), 0, 23]-NRT-code), using
- complete OOA / dual of NRT-code with only one code word [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(7⁶¹, 43, F₇, 2, 34) (dual of [(43, 2), 25, 35]-NRT-code)	[i]		Truncation for OOAs
2	Linear OOA(7⁶⁰, 43, F₇, 2, 33) (dual of [(43, 2), 26, 34]-NRT-code)	[i]		Truncation for OOAs