MinT - Information on Result #1021782

Information on Result #1021782

Linear OOA(7⁷³, 36, F₇, 3, 41) (dual of [(36, 3), 35, 42]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(7⁶, 6, F₇, 3, 6) (dual of [(6, 3), 12, 7]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(7⁶, 7, F₇, 3, 6) (dual of [(7, 3), 15, 7]-NRT-code), using
  - Reedâ€“Solomon NRT-code RS(3;15,7) [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(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(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(7⁷³, 36, F₇, 3, 40) (dual of [(36, 3), 35, 41]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(7⁷⁴, 36, F₇, 3, 41) (dual of [(36, 3), 34, 42]-NRT-code)	[i]		OOA Duplication