MinT - Information on Result #913208

Information on Result #913208

Linear OOA(3²²⁴, 140, F₃, 2, 109) (dual of [(140, 2), 56, 110]-NRT-code), using concatenation of two NRT-codes based on

linear OA(81²¹, 35, F₈₁, 21) (dual of [35, 14, 22]-code or 35-arc in PG(20,81)), using
- discarding factors / shortening the dual code based on linear OA(81²¹, 81, F₈₁, 21) (dual of [81, 60, 22]-code or 81-arc in PG(20,81)), using
  - Reedâ€“Solomon code RS(60,81) [i]
linear OOA(3⁴, 4, F₃, 2, 4) (dual of [(4, 2), 4, 5]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(2;4,3) [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(3²²⁴, 140, F₃, 2, 108) (dual of [(140, 2), 56, 109]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(3²²⁴, 140, F₃, 2, 107) (dual of [(140, 2), 56, 108]-NRT-code)	[i]
3	Linear OOA(3²²⁴, 140, F₃, 2, 106) (dual of [(140, 2), 56, 107]-NRT-code)	[i]
4	Linear OOA(3²²⁶, 141, F₃, 2, 109) (dual of [(141, 2), 56, 110]-NRT-code)	[i]		NRT-Code Embedding in Larger Space
5	Linear OOA(3²²⁵, 140, F₃, 2, 109) (dual of [(140, 2), 55, 110]-NRT-code)	[i]		OOA Duplication
6	Linear OOA(3²²³, 139, F₃, 2, 108) (dual of [(139, 2), 55, 109]-NRT-code)	[i]		Truncation for OOAs
7	Linear OOA(3²²², 139, F₃, 2, 107) (dual of [(139, 2), 56, 108]-NRT-code)	[i]
8	Linear OOA(3²²¹, 138, F₃, 2, 106) (dual of [(138, 2), 55, 107]-NRT-code)	[i]
9	Linear OOA(3²²⁰, 138, F₃, 2, 105) (dual of [(138, 2), 56, 106]-NRT-code)	[i]
10	Linear OOA(3²¹⁹, 137, F₃, 2, 104) (dual of [(137, 2), 55, 105]-NRT-code)	[i]
11	Linear OOA(3²¹⁸, 137, F₃, 2, 103) (dual of [(137, 2), 56, 104]-NRT-code)	[i]
12	Linear OOA(3²¹⁷, 136, F₃, 2, 102) (dual of [(136, 2), 55, 103]-NRT-code)	[i]
13	Linear OOA(3²²⁴, 70, F₃, 4, 109) (dual of [(70, 4), 56, 110]-NRT-code)	[i]		OOA Folding