MinT - Information on Result #913196

Information on Result #913196

Linear OOA(3²¹⁶, 136, F₃, 2, 104) (dual of [(136, 2), 56, 105]-NRT-code), using concatenation of two NRT-codes based on

linear OA(81²⁰, 34, F₈₁, 20) (dual of [34, 14, 21]-code or 34-arc in PG(19,81)), using
- discarding factors / shortening the dual code based on linear OA(81²⁰, 81, F₈₁, 20) (dual of [81, 61, 21]-code or 81-arc in PG(19,81)), using
  - Reedâ€“Solomon code RS(61,81) [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(3²¹⁶, 136, F₃, 2, 103) (dual of [(136, 2), 56, 104]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(3²¹⁶, 136, F₃, 2, 102) (dual of [(136, 2), 56, 103]-NRT-code)	[i]		Strength Reduction for OOAs
3	Linear OOA(3²¹⁸, 137, F₃, 2, 104) (dual of [(137, 2), 56, 105]-NRT-code)	[i]		NRT-Code Embedding in Larger Space
4	Linear OOA(3²¹⁷, 136, F₃, 2, 104) (dual of [(136, 2), 55, 105]-NRT-code)	[i]		OOA Duplication
5	Linear OOA(3²¹⁵, 135, F₃, 2, 103) (dual of [(135, 2), 55, 104]-NRT-code)	[i]		Truncation for OOAs
6	Linear OOA(3²¹⁴, 135, F₃, 2, 102) (dual of [(135, 2), 56, 103]-NRT-code)	[i]
7	Linear OOA(3²¹³, 134, F₃, 2, 101) (dual of [(134, 2), 55, 102]-NRT-code)	[i]
8	Linear OOA(3²¹², 134, F₃, 2, 100) (dual of [(134, 2), 56, 101]-NRT-code)	[i]
9	Linear OOA(3²¹¹, 133, F₃, 2, 99) (dual of [(133, 2), 55, 100]-NRT-code)	[i]
10	Linear OOA(3²¹⁰, 133, F₃, 2, 98) (dual of [(133, 2), 56, 99]-NRT-code)	[i]
11	Linear OOA(3²⁰⁹, 132, F₃, 2, 97) (dual of [(132, 2), 55, 98]-NRT-code)	[i]
12	Linear OOA(3²¹⁶, 68, F₃, 4, 104) (dual of [(68, 4), 56, 105]-NRT-code)	[i]		OOA Folding