MinT - Information on Result #916113

Information on Result #916113

Linear OOA(3¹⁹⁸, 116, F₃, 2, 113) (dual of [(116, 2), 34, 114]-NRT-code), using concatenation of two NRT-codes based on

linear OOA(9⁴¹, 29, F₉, 2, 37) (dual of [(29, 2), 17, 38]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(9⁴¹, 30, F₉, 2, 37) (dual of [(30, 2), 19, 38]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,22P) [i] based on function field F/F₉ with g(F) = 4 and N(F) ≥ 30, 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(3¹⁹⁸, 116, F₃, 2, 112) (dual of [(116, 2), 34, 113]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(3¹⁹⁸, 116, F₃, 2, 111) (dual of [(116, 2), 34, 112]-NRT-code)	[i]		Strength Reduction for OOAs
3	Linear OOA(3¹⁹⁹, 116, F₃, 2, 113) (dual of [(116, 2), 33, 114]-NRT-code)	[i]		OOA Duplication
4	Linear OOA(3¹⁹⁷, 115, F₃, 2, 112) (dual of [(115, 2), 33, 113]-NRT-code)	[i]		Truncation for OOAs
5	Linear OOA(3¹⁹⁶, 115, F₃, 2, 111) (dual of [(115, 2), 34, 112]-NRT-code)	[i]
6	Linear OOA(3¹⁹⁵, 114, F₃, 2, 110) (dual of [(114, 2), 33, 111]-NRT-code)	[i]
7	Linear OOA(3¹⁹⁴, 114, F₃, 2, 109) (dual of [(114, 2), 34, 110]-NRT-code)	[i]
8	Linear OOA(3¹⁹³, 113, F₃, 2, 108) (dual of [(113, 2), 33, 109]-NRT-code)	[i]
9	Linear OOA(3¹⁹⁸, 58, F₃, 4, 113) (dual of [(58, 4), 34, 114]-NRT-code)	[i]		OOA Folding