MinT - Information on Result #1027719

Information on Result #1027719

Linear OOA(7¹⁰⁹, 37, F₇, 3, 104) (dual of [(37, 3), 2, 105]-NRT-code), using juxtaposition based on

linear OOA(7⁴, 2, F₇, 3, 4) (dual of [(2, 3), 2, 5]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(7⁴, 7, F₇, 3, 4) (dual of [(7, 3), 17, 5]-NRT-code), using
  - Reedâ€“Solomon NRT-code RS(3;17,7) [i]
linear OOA(7¹⁰³, 35, F₇, 3, 99) (dual of [(35, 3), 2, 100]-NRT-code), using
- repeating each code word 5 times [i] based on linear OOA(7¹⁹, 7, F₇, 3, 19) (dual of [(7, 3), 2, 20]-NRT-code), using
  - Reedâ€“Solomon NRT-code RS(3;2,7) [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(7¹⁰⁹, 37, F₇, 3, 103) (dual of [(37, 3), 2, 104]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(7¹⁰⁹, 37, F₇, 3, 102) (dual of [(37, 3), 2, 103]-NRT-code)	[i]
3	Linear OOA(7¹⁰⁹, 37, F₇, 3, 101) (dual of [(37, 3), 2, 102]-NRT-code)	[i]
4	Linear OOA(7¹⁰⁹, 37, F₇, 3, 100) (dual of [(37, 3), 2, 101]-NRT-code)	[i]
5	Linear OOA(7¹⁰⁹, 37, F₇, 3, 99) (dual of [(37, 3), 2, 100]-NRT-code)	[i]
6	Linear OOA(7¹⁰⁹, 37, F₇, 3, 98) (dual of [(37, 3), 2, 99]-NRT-code)	[i]
7	Linear OOA(7¹⁰⁹, 37, F₇, 3, 97) (dual of [(37, 3), 2, 98]-NRT-code)	[i]
8	Linear OOA(7¹⁰⁰, 34, F₇, 3, 95) (dual of [(34, 3), 2, 96]-NRT-code)	[i]		Truncation for OOAs
9	Linear OOA(7⁹⁷, 33, F₇, 3, 92) (dual of [(33, 3), 2, 93]-NRT-code)	[i]
10	Linear OOA(7⁹¹, 31, F₇, 3, 86) (dual of [(31, 3), 2, 87]-NRT-code)	[i]
11	Linear OOA(7⁸⁵, 29, F₇, 3, 80) (dual of [(29, 3), 2, 81]-NRT-code)	[i]
12	Linear OOA(7⁷⁹, 27, F₇, 3, 74) (dual of [(27, 3), 2, 75]-NRT-code)	[i]
13	Linear OOA(7⁷⁶, 26, F₇, 3, 71) (dual of [(26, 3), 2, 72]-NRT-code)	[i]