MinT - Information on Result #906487

Information on Result #906487

Linear OOA(7⁷⁴, 42, F₇, 2, 54) (dual of [(42, 2), 10, 55]-NRT-code), using generalized (u,Â u+v)-construction based on

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(7⁹, 6, F₇, 2, 9) (dual of [(6, 2), 3, 10]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(7⁹, 7, F₇, 2, 9) (dual of [(7, 2), 5, 10]-NRT-code), using
  - Reedâ€“Solomon NRT-code RS(2;5,7) [i]
linear OOA(7¹⁰, 6, F₇, 2, 10) (dual of [(6, 2), 2, 11]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(7¹⁰, 7, F₇, 2, 10) (dual of [(7, 2), 4, 11]-NRT-code), using
  - Reedâ€“Solomon NRT-code RS(2;4,7) [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)
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(7⁷⁴, 42, F₇, 2, 53) (dual of [(42, 2), 10, 54]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(7⁷⁴, 42, F₇, 2, 52) (dual of [(42, 2), 10, 53]-NRT-code)	[i]		Strength Reduction for OOAs