MinT - Information on Result #1021689

Information on Result #1021689

Linear OOA(7⁸³, 35, F₇, 3, 53) (dual of [(35, 3), 22, 54]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(7⁷, 5, F₇, 3, 7) (dual of [(5, 3), 8, 8]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(7⁷, 7, F₇, 3, 7) (dual of [(7, 3), 14, 8]-NRT-code), using
  - Reedâ€“Solomon NRT-code RS(3;14,7) [i]
linear OOA(7⁸, 5, F₇, 3, 8) (dual of [(5, 3), 7, 9]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(7⁸, 7, F₇, 3, 8) (dual of [(7, 3), 13, 9]-NRT-code), using
  - Reedâ€“Solomon NRT-code RS(3;13,7) [i]
linear OOA(7¹⁰, 5, F₇, 3, 10) (dual of [(5, 3), 5, 11]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(7¹⁰, 7, F₇, 3, 10) (dual of [(7, 3), 11, 11]-NRT-code), using
  - Reedâ€“Solomon NRT-code RS(3;11,7) [i]
linear OOA(7¹³, 5, F₇, 3, 13) (dual of [(5, 3), 2, 14]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(7¹³, 7, F₇, 3, 13) (dual of [(7, 3), 8, 14]-NRT-code), using
  - Reedâ€“Solomon NRT-code RS(3;8,7) [i]
linear OOA(7¹⁵, 5, F₇, 3, 15) (dual of [(5, 3), 0, 16]-NRT-code), using
- complete OOA / dual of NRT-code with only one code word [i]
linear OOA(7¹⁵, 5, F₇, 3, 15) (dual of [(5, 3), 0, 16]-NRT-code) (see above)
linear OOA(7¹⁵, 5, F₇, 3, 15) (dual of [(5, 3), 0, 16]-NRT-code) (see above)

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(7⁸³, 35, F₇, 3, 52) (dual of [(35, 3), 22, 53]-NRT-code)	[i]		Strength Reduction for OOAs