MinT - Information on Result #1021773

Information on Result #1021773

Linear OOA(7⁸¹, 36, F₇, 3, 49) (dual of [(36, 3), 27, 50]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(7⁸, 6, F₇, 3, 8) (dual of [(6, 3), 10, 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(7⁹, 6, F₇, 3, 9) (dual of [(6, 3), 9, 10]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(7⁹, 7, F₇, 3, 9) (dual of [(7, 3), 12, 10]-NRT-code), using
  - Reedâ€“Solomon NRT-code RS(3;12,7) [i]
linear OOA(7¹², 6, F₇, 3, 12) (dual of [(6, 3), 6, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(7¹², 7, F₇, 3, 12) (dual of [(7, 3), 9, 13]-NRT-code), using
  - Reedâ€“Solomon NRT-code RS(3;9,7) [i]
linear OOA(7¹⁶, 6, F₇, 3, 16) (dual of [(6, 3), 2, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(7¹⁶, 7, F₇, 3, 16) (dual of [(7, 3), 5, 17]-NRT-code), using
  - Reedâ€“Solomon NRT-code RS(3;5,7) [i]
linear OOA(7¹⁸, 6, F₇, 3, 18) (dual of [(6, 3), 0, 19]-NRT-code), using
- complete OOA / dual of NRT-code with only one code word [i]
linear OOA(7¹⁸, 6, F₇, 3, 18) (dual of [(6, 3), 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(7⁸¹, 36, F₇, 3, 48) (dual of [(36, 3), 27, 49]-NRT-code)	[i]		Strength Reduction for OOAs