MinT - Information on Result #915982

Information on Result #915982

Linear OOA(3⁹⁰, 52, F₃, 2, 56) (dual of [(52, 2), 14, 57]-NRT-code), using concatenation of two NRT-codes based on

linear OOA(9¹⁹, 13, F₉, 2, 18) (dual of [(13, 2), 7, 19]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(9¹⁹, 16, F₉, 2, 18) (dual of [(16, 2), 13, 19]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,13P) [i] based on function field F/F₉ with g(F) = 1 and N(F) ≥ 16, using
    - a function field by GarcÃa and Quoos [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(3⁹⁰, 52, F₃, 2, 55) (dual of [(52, 2), 14, 56]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(3⁹⁰, 52, F₃, 2, 54) (dual of [(52, 2), 14, 55]-NRT-code)	[i]		Strength Reduction for OOAs
3	Linear OOA(3⁹¹, 52, F₃, 2, 56) (dual of [(52, 2), 13, 57]-NRT-code)	[i]		OOA Duplication
4	Linear OOA(3⁸⁹, 51, F₃, 2, 55) (dual of [(51, 2), 13, 56]-NRT-code)	[i]		Truncation for OOAs
5	Linear OOA(3⁸⁸, 51, F₃, 2, 54) (dual of [(51, 2), 14, 55]-NRT-code)	[i]
6	Linear OOA(3⁸⁷, 50, F₃, 2, 53) (dual of [(50, 2), 13, 54]-NRT-code)	[i]
7	Linear OOA(3⁸⁶, 50, F₃, 2, 52) (dual of [(50, 2), 14, 53]-NRT-code)	[i]
8	Linear OOA(3⁸⁵, 49, F₃, 2, 51) (dual of [(49, 2), 13, 52]-NRT-code)	[i]
9	Linear OOA(3⁸⁴, 49, F₃, 2, 50) (dual of [(49, 2), 14, 51]-NRT-code)	[i]
10	Linear OOA(3⁹⁰, 26, F₃, 4, 56) (dual of [(26, 4), 14, 57]-NRT-code)	[i]		OOA Folding