MinT - Information on Result #916139

Information on Result #916139

Linear OOA(3²²⁴, 136, F₃, 2, 116) (dual of [(136, 2), 48, 117]-NRT-code), using concatenation of two NRT-codes based on

linear OOA(9⁴⁴, 34, F₉, 2, 38) (dual of [(34, 2), 24, 39]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,29P) [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(3²²⁴, 136, F₃, 2, 115) (dual of [(136, 2), 48, 116]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(3²²⁶, 137, F₃, 2, 116) (dual of [(137, 2), 48, 117]-NRT-code)	[i]		NRT-Code Embedding in Larger Space
3	Linear OOA(3²²⁸, 138, F₃, 2, 116) (dual of [(138, 2), 48, 117]-NRT-code)	[i]		NRT-Code Embedding in Larger Space
4	Linear OOA(3²²⁵, 136, F₃, 2, 116) (dual of [(136, 2), 47, 117]-NRT-code)	[i]		OOA Duplication
5	Linear OOA(3²²³, 135, F₃, 2, 115) (dual of [(135, 2), 47, 116]-NRT-code)	[i]		Truncation for OOAs
6	Linear OOA(3²²², 135, F₃, 2, 114) (dual of [(135, 2), 48, 115]-NRT-code)	[i]
7	Linear OOA(3²²¹, 134, F₃, 2, 113) (dual of [(134, 2), 47, 114]-NRT-code)	[i]
8	Linear OOA(3²²⁰, 134, F₃, 2, 112) (dual of [(134, 2), 48, 113]-NRT-code)	[i]
9	Linear OOA(3²¹⁹, 133, F₃, 2, 111) (dual of [(133, 2), 47, 112]-NRT-code)	[i]
10	Linear OOA(3²¹⁸, 133, F₃, 2, 110) (dual of [(133, 2), 48, 111]-NRT-code)	[i]
11	Linear OOA(3²¹⁷, 132, F₃, 2, 109) (dual of [(132, 2), 47, 110]-NRT-code)	[i]
12	Linear OOA(3²²⁴, 68, F₃, 4, 116) (dual of [(68, 4), 48, 117]-NRT-code)	[i]		OOA Folding