MinT - Information on Result #1027715

Information on Result #1027715

Linear OOA(7¹⁰⁸, 37, F₇, 3, 100) (dual of [(37, 3), 3, 101]-NRT-code), using juxtaposition based on

linear OOA(7¹², 5, F₇, 3, 12) (dual of [(5, 3), 3, 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(7⁹³, 32, F₇, 3, 87) (dual of [(32, 3), 3, 88]-NRT-code), using
- repeating each code word 4 times [i] based on linear OOA(7²¹, 8, F₇, 3, 21) (dual of [(8, 3), 3, 22]-NRT-code), using
  - extended Reedâ€“Solomon NRT-code RS_e(3;3,7) [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(7¹⁰⁸, 37, F₇, 3, 99) (dual of [(37, 3), 3, 100]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(7¹⁰⁰, 34, F₇, 3, 92) (dual of [(34, 3), 2, 93]-NRT-code)	[i]		Truncation for OOAs
3	Linear OOA(7⁹⁹, 34, F₇, 3, 91) (dual of [(34, 3), 3, 92]-NRT-code)	[i]
4	Linear OOA(7⁹⁷, 33, F₇, 3, 89) (dual of [(33, 3), 2, 90]-NRT-code)	[i]
5	Linear OOA(7⁹¹, 31, F₇, 3, 83) (dual of [(31, 3), 2, 84]-NRT-code)	[i]
6	Linear OOA(7⁹⁰, 31, F₇, 3, 82) (dual of [(31, 3), 3, 83]-NRT-code)	[i]
7	Linear OOA(7⁸⁵, 29, F₇, 3, 77) (dual of [(29, 3), 2, 78]-NRT-code)	[i]
8	Linear OOA(7⁸⁴, 29, F₇, 3, 76) (dual of [(29, 3), 3, 77]-NRT-code)	[i]
9	Linear OOA(7⁷⁸, 27, F₇, 3, 70) (dual of [(27, 3), 3, 71]-NRT-code)	[i]
10	Linear OOA(7⁷⁶, 26, F₇, 3, 68) (dual of [(26, 3), 2, 69]-NRT-code)	[i]
11	Linear OOA(7⁷⁵, 26, F₇, 3, 67) (dual of [(26, 3), 3, 68]-NRT-code)	[i]