MinT - Information on Result #1021853

Information on Result #1021853

Linear OOA(7⁸⁸, 44, F₇, 3, 47) (dual of [(44, 3), 44, 48]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(7⁹, 8, F₇, 3, 9) (dual of [(8, 3), 15, 10]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(3;15,7) [i]
linear OOA(7¹², 9, F₇, 3, 11) (dual of [(9, 3), 15, 12]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(7¹², 13, F₇, 3, 11) (dual of [(13, 3), 27, 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, using
      - a shift-net [i]
linear OOA(7¹⁶, 9, F₇, 3, 15) (dual of [(9, 3), 11, 16]-NRT-code), using
- extracting embedded OOA [i] based on digital (1, 16, 9)-net over F₇, using
  - net from sequence [i] based on digital (1, 8)-sequence over F₇, using
    - Niederreiter sequence [i]
linear OOA(7²⁴, 9, F₇, 3, 23) (dual of [(9, 3), 3, 24]-NRT-code), using
- extracting embedded OOA [i] based on digital (1, 24, 9)-net over F₇, using
  - net from sequence [i] based on digital (1, 8)-sequence over F₇ (see above)
linear OOA(7²⁷, 9, F₇, 3, 27) (dual of [(9, 3), 0, 28]-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(7⁸⁷, 43, F₇, 3, 46) (dual of [(43, 3), 42, 47]-NRT-code)	[i]		Truncation for OOAs
2	Linear OOA(7⁸⁶, 43, F₇, 3, 45) (dual of [(43, 3), 43, 46]-NRT-code)	[i]		Truncation for OOAs