MinT - Information on Result #1021665

Information on Result #1021665

Linear OOA(7¹⁰², 42, F₇, 3, 65) (dual of [(42, 3), 24, 66]-NRT-code), using generalized (u,Â u+v)-construction based on

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(7¹⁰, 6, F₇, 3, 10) (dual of [(6, 3), 8, 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, 6, F₇, 3, 13) (dual of [(6, 3), 5, 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(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)
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(7¹⁰², 42, F₇, 3, 64) (dual of [(42, 3), 24, 65]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(7¹⁰², 42, F₇, 3, 63) (dual of [(42, 3), 24, 64]-NRT-code)	[i]		Strength Reduction for OOAs