MinT - Information on Result #1021765

Information on Result #1021765

Linear OOA(7⁸⁴, 36, F₇, 3, 53) (dual of [(36, 3), 24, 54]-NRT-code), using generalized (u,Â u+v)-construction based on

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(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(7¹⁷, 6, F₇, 3, 17) (dual of [(6, 3), 1, 18]-NRT-code), using
- dual of repetition NRT-code with length 6 [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(7⁸⁴, 36, F₇, 3, 52) (dual of [(36, 3), 24, 53]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(7⁸⁵, 36, F₇, 3, 53) (dual of [(36, 3), 23, 54]-NRT-code)	[i]		OOA Duplication