MinT - Information on Result #912775

Information on Result #912775

Linear OOA(3¹²⁴, 68, F₃, 2, 83) (dual of [(68, 2), 12, 84]-NRT-code), using concatenation of two NRT-codes based on

linear OA(27¹³, 17, F₂₇, 13) (dual of [17, 4, 14]-code or 17-arc in PG(12,27)), using
- discarding factors / shortening the dual code based on linear OA(27¹³, 27, F₂₇, 13) (dual of [27, 14, 14]-code or 27-arc in PG(12,27)), using
  - Reedâ€“Solomon code RS(14,27) [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(3¹²⁴, 68, F₃, 2, 82) (dual of [(68, 2), 12, 83]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(3¹²⁴, 68, F₃, 2, 81) (dual of [(68, 2), 12, 82]-NRT-code)	[i]
3	Linear OOA(3¹²⁴, 68, F₃, 2, 80) (dual of [(68, 2), 12, 81]-NRT-code)	[i]
4	Linear OOA(3¹²⁴, 68, F₃, 2, 79) (dual of [(68, 2), 12, 80]-NRT-code)	[i]
5	Linear OOA(3¹²⁵, 68, F₃, 2, 83) (dual of [(68, 2), 11, 84]-NRT-code)	[i]		OOA Duplication
6	Linear OOA(3¹²³, 67, F₃, 2, 82) (dual of [(67, 2), 11, 83]-NRT-code)	[i]		Truncation for OOAs
7	Linear OOA(3¹²², 67, F₃, 2, 81) (dual of [(67, 2), 12, 82]-NRT-code)	[i]
8	Linear OOA(3¹²¹, 66, F₃, 2, 80) (dual of [(66, 2), 11, 81]-NRT-code)	[i]
9	Linear OOA(3¹²⁰, 66, F₃, 2, 79) (dual of [(66, 2), 12, 80]-NRT-code)	[i]
10	Linear OOA(3¹¹⁹, 65, F₃, 2, 78) (dual of [(65, 2), 11, 79]-NRT-code)	[i]
11	Linear OOA(3¹¹⁸, 65, F₃, 2, 77) (dual of [(65, 2), 12, 78]-NRT-code)	[i]
12	Linear OOA(3¹¹⁷, 64, F₃, 2, 76) (dual of [(64, 2), 11, 77]-NRT-code)	[i]
13	Linear OOA(3¹²⁴, 34, F₃, 4, 83) (dual of [(34, 4), 12, 84]-NRT-code)	[i]		OOA Folding