MinT - Information on Result #1030673

Information on Result #1030673

Linear OOA(3²³⁰, 84, F₃, 3, 149) (dual of [(84, 3), 22, 150]-NRT-code), using concatenation of two NRT-codes based on

linear OOA(9⁵², 21, F₉, 3, 49) (dual of [(21, 3), 11, 50]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(9⁵², 28, F₉, 3, 49) (dual of [(28, 3), 32, 50]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,34P) [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(3²³⁰, 84, F₃, 3, 148) (dual of [(84, 3), 22, 149]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(3²³⁰, 84, F₃, 3, 147) (dual of [(84, 3), 22, 148]-NRT-code)	[i]		Strength Reduction for OOAs
3	Linear OOA(3²²⁹, 83, F₃, 3, 148) (dual of [(83, 3), 20, 149]-NRT-code)	[i]		Truncation for OOAs
4	Linear OOA(3²²⁸, 83, F₃, 3, 147) (dual of [(83, 3), 21, 148]-NRT-code)	[i]
5	Linear OOA(3²²⁷, 83, F₃, 3, 146) (dual of [(83, 3), 22, 147]-NRT-code)	[i]
6	Linear OOA(3²²⁶, 82, F₃, 3, 145) (dual of [(82, 3), 20, 146]-NRT-code)	[i]
7	Linear OOA(3²²⁵, 82, F₃, 3, 144) (dual of [(82, 3), 21, 145]-NRT-code)	[i]
8	Linear OOA(3²²⁴, 82, F₃, 3, 143) (dual of [(82, 3), 22, 144]-NRT-code)	[i]
9	Linear OOA(3²²³, 81, F₃, 3, 142) (dual of [(81, 3), 20, 143]-NRT-code)	[i]
10	Linear OOA(3²²¹, 81, F₃, 3, 140) (dual of [(81, 3), 22, 141]-NRT-code)	[i]