MinT - Information on Result #906465

Information on Result #906465

Linear OOA(7¹⁰⁶, 62, F₇, 2, 69) (dual of [(62, 2), 18, 70]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(7⁹, 8, F₇, 2, 9) (dual of [(8, 2), 7, 10]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(2;7,7) [i]
linear OOA(7¹², 9, F₇, 2, 11) (dual of [(9, 2), 6, 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, using
      - a shift-net [i]
linear OOA(7¹⁴, 9, F₇, 2, 13) (dual of [(9, 2), 4, 14]-NRT-code), using
- extracting embedded OOA [i] based on digital (1, 14, 9)-net over F₇, using
  - net from sequence [i] based on digital (1, 8)-sequence over F₇, using
    - Niederreiter sequence [i]
linear OOA(7¹⁷, 9, F₇, 2, 17) (dual of [(9, 2), 1, 18]-NRT-code), using
- dual of repetition NRT-code with length 9 [i]
linear OOA(7¹⁸, 9, F₇, 2, 18) (dual of [(9, 2), 0, 19]-NRT-code), using
- complete OOA / dual of NRT-code with only one code word [i]
linear OOA(7¹⁸, 9, F₇, 2, 18) (dual of [(9, 2), 0, 19]-NRT-code) (see above)
linear OOA(7¹⁸, 9, F₇, 2, 18) (dual of [(9, 2), 0, 19]-NRT-code) (see above)

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(7¹⁰⁴, 61, F₇, 2, 67) (dual of [(61, 2), 18, 68]-NRT-code)	[i]		Truncation for OOAs
2	Linear OOA(7¹⁰³, 60, F₇, 2, 66) (dual of [(60, 2), 17, 67]-NRT-code)	[i]		Truncation for OOAs