MinT - Information on Result #912292

Information on Result #912292

Linear OOA(3¹³², 68, F₃, 2, 104) (dual of [(68, 2), 4, 105]-NRT-code), using concatenation of two NRT-codes based on

linear OA(9¹⁵, 17, F₉, 14) (dual of [17, 2, 15]-code), using
- 3 times truncation [i] based on linear OA(9¹⁸, 20, F₉, 17) (dual of [20, 2, 18]-code), using
  - repeating each code word 2 times [i] based on linear OA(9⁸, 10, F₉, 8) (dual of [10, 2, 9]-code or 10-arc in PG(7,9)), using
    - extended Reedâ€“Solomon code RS_e(2,9) [i]
    - Simplex code S(2,9) [i]
linear OOA(3⁶, 4, F₃, 2, 6) (dual of [(4, 2), 2, 7]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(2;2,3) [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(3¹³², 68, F₃, 2, 103) (dual of [(68, 2), 4, 104]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(3¹³², 68, F₃, 2, 102) (dual of [(68, 2), 4, 103]-NRT-code)	[i]
3	Linear OOA(3¹³², 68, F₃, 2, 101) (dual of [(68, 2), 4, 102]-NRT-code)	[i]
4	Linear OOA(3¹³², 68, F₃, 2, 100) (dual of [(68, 2), 4, 101]-NRT-code)	[i]
5	Linear OOA(3¹³², 68, F₃, 2, 99) (dual of [(68, 2), 4, 100]-NRT-code)	[i]
6	Linear OOA(3¹³², 68, F₃, 2, 98) (dual of [(68, 2), 4, 99]-NRT-code)	[i]
7	Linear OOA(3¹³², 68, F₃, 2, 97) (dual of [(68, 2), 4, 98]-NRT-code)	[i]
8	Linear OOA(3¹³⁰, 67, F₃, 2, 102) (dual of [(67, 2), 4, 103]-NRT-code)	[i]		Truncation for OOAs
9	Linear OOA(3¹²⁸, 66, F₃, 2, 100) (dual of [(66, 2), 4, 101]-NRT-code)	[i]
10	Linear OOA(3¹²⁶, 65, F₃, 2, 98) (dual of [(65, 2), 4, 99]-NRT-code)	[i]
11	Linear OOA(3¹²², 63, F₃, 2, 94) (dual of [(63, 2), 4, 95]-NRT-code)	[i]
12	Linear OOA(3¹²¹, 62, F₃, 2, 93) (dual of [(62, 2), 3, 94]-NRT-code)	[i]
13	Linear OOA(3¹²⁰, 62, F₃, 2, 92) (dual of [(62, 2), 4, 93]-NRT-code)	[i]
14	Linear OOA(3¹⁰⁷, 55, F₃, 2, 79) (dual of [(55, 2), 3, 80]-NRT-code)	[i]
15	Linear OOA(3¹³², 34, F₃, 4, 104) (dual of [(34, 4), 4, 105]-NRT-code)	[i]		OOA Folding