MinT - Information on Result #912766

Information on Result #912766

Linear OOA(3¹²¹, 68, F₃, 2, 77) (dual of [(68, 2), 15, 78]-NRT-code), using concatenation of two NRT-codes based on

linear OA(27¹², 17, F₂₇, 12) (dual of [17, 5, 13]-code or 17-arc in PG(11,27)), using
- discarding factors / shortening the dual code based on linear OA(27¹², 27, F₂₇, 12) (dual of [27, 15, 13]-code or 27-arc in PG(11,27)), using
  - Reedâ€“Solomon code RS(15,27) [i]
linear OOA(3⁵, 4, F₃, 2, 5) (dual of [(4, 2), 3, 6]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(2;3,3) [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(3¹²¹, 68, F₃, 2, 76) (dual of [(68, 2), 15, 77]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(3¹²¹, 68, F₃, 2, 75) (dual of [(68, 2), 15, 76]-NRT-code)	[i]
3	Linear OOA(3¹²¹, 68, F₃, 2, 74) (dual of [(68, 2), 15, 75]-NRT-code)	[i]
4	Linear OOA(3¹²¹, 68, F₃, 2, 73) (dual of [(68, 2), 15, 74]-NRT-code)	[i]
5	Linear OOA(3¹²², 68, F₃, 2, 77) (dual of [(68, 2), 14, 78]-NRT-code)	[i]		OOA Duplication
6	Linear OOA(3¹²⁰, 67, F₃, 2, 76) (dual of [(67, 2), 14, 77]-NRT-code)	[i]		Truncation for OOAs
7	Linear OOA(3¹¹⁹, 67, F₃, 2, 75) (dual of [(67, 2), 15, 76]-NRT-code)	[i]
8	Linear OOA(3¹¹⁸, 66, F₃, 2, 74) (dual of [(66, 2), 14, 75]-NRT-code)	[i]
9	Linear OOA(3¹¹⁷, 66, F₃, 2, 73) (dual of [(66, 2), 15, 74]-NRT-code)	[i]
10	Linear OOA(3¹¹⁶, 65, F₃, 2, 72) (dual of [(65, 2), 14, 73]-NRT-code)	[i]
11	Linear OOA(3¹¹⁵, 65, F₃, 2, 71) (dual of [(65, 2), 15, 72]-NRT-code)	[i]
12	Linear OOA(3¹²¹, 34, F₃, 4, 77) (dual of [(34, 4), 15, 78]-NRT-code)	[i]		OOA Folding