MinT - Information on Result #2434656

Information on Result #2434656

Linear OOA(3¹⁹², 112, F₃, 2, 112) (dual of [(112, 2), 32, 113]-NRT-code), using strength reduction based on linear OOA(3¹⁹², 112, F₃, 2, 113) (dual of [(112, 2), 32, 114]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(9⁴⁰, 28, F₉, 2, 37) (dual of [(28, 2), 16, 38]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,18P) [i] based on function field F/F₉ with g(F) = 3 and N(F) ≥ 28, using
    - the Hermitian function field over F₉ [i]
2. 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		Method
1	Linear OOA(3¹⁹⁴, 113, F₃, 2, 112) (dual of [(113, 2), 32, 113]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(3¹⁹³, 112, F₃, 2, 112) (dual of [(112, 2), 31, 113]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(3¹⁹¹, 111, F₃, 2, 111) (dual of [(111, 2), 31, 112]-NRT-code)	[i]	Truncation for OOAs
4	Linear OOA(3¹⁹², 56, F₃, 4, 112) (dual of [(56, 4), 32, 113]-NRT-code)	[i]	OOA Folding