MinT - Information on Result #915973

Information on Result #915973

Linear OOA(3⁸⁶, 52, F₃, 2, 50) (dual of [(52, 2), 18, 51]-NRT-code), using concatenation of two NRT-codes based on

linear OOA(9¹⁷, 13, F₉, 2, 16) (dual of [(13, 2), 9, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(9¹⁷, 16, F₉, 2, 16) (dual of [(16, 2), 15, 17]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,15P) [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(3⁸⁶, 52, F₃, 2, 49) (dual of [(52, 2), 18, 50]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(3⁸⁶, 52, F₃, 2, 48) (dual of [(52, 2), 18, 49]-NRT-code)	[i]		Strength Reduction for OOAs
3	Linear OOA(3⁸⁷, 52, F₃, 2, 50) (dual of [(52, 2), 17, 51]-NRT-code)	[i]		OOA Duplication
4	Linear OOA(3⁸⁵, 51, F₃, 2, 49) (dual of [(51, 2), 17, 50]-NRT-code)	[i]		Truncation for OOAs
5	Linear OOA(3⁸⁴, 51, F₃, 2, 48) (dual of [(51, 2), 18, 49]-NRT-code)	[i]
6	Linear OOA(3⁸³, 50, F₃, 2, 47) (dual of [(50, 2), 17, 48]-NRT-code)	[i]
7	Linear OOA(3⁸², 50, F₃, 2, 46) (dual of [(50, 2), 18, 47]-NRT-code)	[i]
8	Linear OOA(3⁸¹, 49, F₃, 2, 45) (dual of [(49, 2), 17, 46]-NRT-code)	[i]
9	Linear OOA(3⁸⁰, 49, F₃, 2, 44) (dual of [(49, 2), 18, 45]-NRT-code)	[i]
10	Linear OOA(3⁸⁶, 26, F₃, 4, 50) (dual of [(26, 4), 18, 51]-NRT-code)	[i]		OOA Folding