MinT - Information on Result #916116

Information on Result #916116

Linear OOA(3²¹⁸, 136, F₃, 2, 107) (dual of [(136, 2), 54, 108]-NRT-code), using concatenation of two NRT-codes based on

linear OOA(9⁴¹, 34, F₉, 2, 35) (dual of [(34, 2), 27, 36]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,32P) [i] based on function field F/F₉ with g(F) = 6 and N(F) ≥ 34, using
  - a function field by SÃ©mirat [i]
linear OA(3², 4, F₃, 2) (dual of [4, 2, 3]-code or 4-arc in PG(1,3)), using
- extended Reedâ€“Solomon code RS_e(2,3) [i]
- Hamming code H(2,3) [i]
- Simplex code S(2,3) [i]
- the Tetracode [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(3²¹⁸, 136, F₃, 2, 106) (dual of [(136, 2), 54, 107]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(3²¹⁸, 136, F₃, 2, 105) (dual of [(136, 2), 54, 106]-NRT-code)	[i]		Strength Reduction for OOAs
3	Linear OOA(3²²⁰, 137, F₃, 2, 107) (dual of [(137, 2), 54, 108]-NRT-code)	[i]		NRT-Code Embedding in Larger Space
4	Linear OOA(3²¹⁹, 136, F₃, 2, 107) (dual of [(136, 2), 53, 108]-NRT-code)	[i]		OOA Duplication
5	Linear OOA(3²¹⁷, 135, F₃, 2, 106) (dual of [(135, 2), 53, 107]-NRT-code)	[i]		Truncation for OOAs
6	Linear OOA(3²¹⁶, 135, F₃, 2, 105) (dual of [(135, 2), 54, 106]-NRT-code)	[i]
7	Linear OOA(3²¹⁵, 134, F₃, 2, 104) (dual of [(134, 2), 53, 105]-NRT-code)	[i]
8	Linear OOA(3²¹⁴, 134, F₃, 2, 103) (dual of [(134, 2), 54, 104]-NRT-code)	[i]
9	Linear OOA(3²¹³, 133, F₃, 2, 102) (dual of [(133, 2), 53, 103]-NRT-code)	[i]
10	Linear OOA(3²¹², 133, F₃, 2, 101) (dual of [(133, 2), 54, 102]-NRT-code)	[i]
11	Linear OOA(3²¹¹, 132, F₃, 2, 100) (dual of [(132, 2), 53, 101]-NRT-code)	[i]
12	Linear OOA(3²¹⁸, 68, F₃, 4, 107) (dual of [(68, 4), 54, 108]-NRT-code)	[i]		OOA Folding