MinT - Information on Result #906507

Information on Result #906507

Linear OOA(7⁶⁸, 42, F₇, 2, 44) (dual of [(42, 2), 16, 45]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(7⁶, 6, F₇, 2, 6) (dual of [(6, 2), 6, 7]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(7⁶, 7, F₇, 2, 6) (dual of [(7, 2), 8, 7]-NRT-code), using
  - Reedâ€“Solomon NRT-code RS(2;8,7) [i]
linear OOA(7⁷, 6, F₇, 2, 7) (dual of [(6, 2), 5, 8]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(7⁷, 7, F₇, 2, 7) (dual of [(7, 2), 7, 8]-NRT-code), using
  - Reedâ€“Solomon NRT-code RS(2;7,7) [i]
linear OOA(7⁸, 6, F₇, 2, 8) (dual of [(6, 2), 4, 9]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(7⁸, 7, F₇, 2, 8) (dual of [(7, 2), 6, 9]-NRT-code), using
  - Reedâ€“Solomon NRT-code RS(2;6,7) [i]
linear OOA(7¹¹, 6, F₇, 2, 11) (dual of [(6, 2), 1, 12]-NRT-code), using
- dual of repetition NRT-code with length 6 [i]
linear OOA(7¹², 6, F₇, 2, 12) (dual of [(6, 2), 0, 13]-NRT-code), using
- complete OOA / dual of NRT-code with only one code word [i]
linear OOA(7¹², 6, F₇, 2, 12) (dual of [(6, 2), 0, 13]-NRT-code) (see above)
linear OOA(7¹², 6, F₇, 2, 12) (dual of [(6, 2), 0, 13]-NRT-code) (see above)

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(7⁶⁸, 42, F₇, 2, 43) (dual of [(42, 2), 16, 44]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(7⁶⁸, 42, F₇, 2, 42) (dual of [(42, 2), 16, 43]-NRT-code)	[i]		Strength Reduction for OOAs