MinT - Information on Result #1021655

Information on Result #1021655

Linear OOA(7¹⁰⁸, 42, F₇, 3, 74) (dual of [(42, 3), 18, 75]-NRT-code), using generalized (u,Â u+v)-construction based on

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(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(7¹⁴, 6, F₇, 3, 14) (dual of [(6, 3), 4, 15]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(7¹⁴, 7, F₇, 3, 14) (dual of [(7, 3), 7, 15]-NRT-code), using
  - Reedâ€“Solomon NRT-code RS(3;7,7) [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)
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(7¹⁰⁸, 42, F₇, 3, 73) (dual of [(42, 3), 18, 74]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(7¹⁰⁸, 42, F₇, 3, 72) (dual of [(42, 3), 18, 73]-NRT-code)	[i]		Strength Reduction for OOAs