MinT - Information on Result #1021778

Information on Result #1021778

Linear OOA(7⁷⁶, 36, F₇, 3, 44) (dual of [(36, 3), 32, 45]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(7⁷, 6, F₇, 3, 7) (dual of [(6, 3), 11, 8]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(7⁷, 7, F₇, 3, 7) (dual of [(7, 3), 14, 8]-NRT-code), using
  - Reedâ€“Solomon NRT-code RS(3;14,7) [i]
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(7¹¹, 6, F₇, 3, 11) (dual of [(6, 3), 7, 12]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(7¹¹, 7, F₇, 3, 11) (dual of [(7, 3), 10, 12]-NRT-code), using
  - Reedâ€“Solomon NRT-code RS(3;10,7) [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)

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(7⁷⁶, 36, F₇, 3, 43) (dual of [(36, 3), 32, 44]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(7⁷⁷, 36, F₇, 3, 44) (dual of [(36, 3), 31, 45]-NRT-code)	[i]		OOA Duplication