MinT - Information on Result #941493

Information on Result #941493

Linear OOA(7⁶⁵, 44, F₇, 2, 38) (dual of [(44, 2), 23, 39]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(7¹⁰, 11, F₇, 2, 9) (dual of [(11, 2), 12, 10]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(7¹⁰, 13, F₇, 2, 9) (dual of [(13, 2), 16, 10]-NRT-code), using
  - extracting embedded OOA [i] based on digital (1, 10, 13)-net over F₇, using
    - 3 times m-reduction [i] based on digital (1, 13, 13)-net over F₇, using
      - a shift-net [i]
linear OOA(7¹³, 11, F₇, 2, 12) (dual of [(11, 2), 9, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(7¹³, 13, F₇, 2, 12) (dual of [(13, 2), 13, 13]-NRT-code), using
  - extracting embedded OOA [i] based on digital (1, 13, 13)-net over F₇ (see above)
linear OOA(7²⁰, 11, F₇, 2, 19) (dual of [(11, 2), 2, 20]-NRT-code), using
- 10 step truncation [i] based on linear OOA(7³⁰, 16, F₇, 2, 29) (dual of [(16, 2), 2, 30]-NRT-code), using
  - repeating each code word 2 times [i] based on linear OOA(7¹⁴, 8, F₇, 2, 14) (dual of [(8, 2), 2, 15]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;2,7) [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(7⁶⁴, 43, F₇, 2, 37) (dual of [(43, 2), 22, 38]-NRT-code)	[i]		Truncation for OOAs
2	Linear OOA(7⁶³, 43, F₇, 2, 36) (dual of [(43, 2), 23, 37]-NRT-code)	[i]		Truncation for OOAs