MinT - Information on Result #916110

Information on Result #916110

Linear OOA(3¹⁹⁰, 108, F₃, 2, 116) (dual of [(108, 2), 26, 117]-NRT-code), using concatenation of two NRT-codes based on

linear OOA(9⁴¹, 27, F₉, 2, 38) (dual of [(27, 2), 13, 39]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(9⁴¹, 28, F₉, 2, 38) (dual of [(28, 2), 15, 39]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,17P) [i] based on function field F/F₉ with g(F) = 3 and N(F) ≥ 28, using
    - the Hermitian function field over F₉ [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(3¹⁹⁰, 108, F₃, 2, 115) (dual of [(108, 2), 26, 116]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(3¹⁹⁰, 108, F₃, 2, 114) (dual of [(108, 2), 26, 115]-NRT-code)	[i]		Strength Reduction for OOAs
3	Linear OOA(3¹⁹¹, 108, F₃, 2, 116) (dual of [(108, 2), 25, 117]-NRT-code)	[i]		OOA Duplication
4	Linear OOA(3¹⁸⁹, 107, F₃, 2, 115) (dual of [(107, 2), 25, 116]-NRT-code)	[i]		Truncation for OOAs
5	Linear OOA(3¹⁸⁸, 107, F₃, 2, 114) (dual of [(107, 2), 26, 115]-NRT-code)	[i]
6	Linear OOA(3¹⁸⁷, 106, F₃, 2, 113) (dual of [(106, 2), 25, 114]-NRT-code)	[i]
7	Linear OOA(3¹⁸⁶, 106, F₃, 2, 112) (dual of [(106, 2), 26, 113]-NRT-code)	[i]
8	Linear OOA(3¹⁸⁵, 105, F₃, 2, 111) (dual of [(105, 2), 25, 112]-NRT-code)	[i]
9	Linear OOA(3¹⁸⁴, 105, F₃, 2, 110) (dual of [(105, 2), 26, 111]-NRT-code)	[i]
10	Linear OOA(3¹⁸³, 104, F₃, 2, 109) (dual of [(104, 2), 25, 110]-NRT-code)	[i]
11	Linear OOA(3¹⁹⁰, 54, F₃, 4, 116) (dual of [(54, 4), 26, 117]-NRT-code)	[i]		OOA Folding