MinT - Information on Result #1030648

Information on Result #1030648

Linear OOA(3²²⁰, 84, F₃, 3, 134) (dual of [(84, 3), 32, 135]-NRT-code), using concatenation of two NRT-codes based on

linear OOA(9⁴⁷, 21, F₉, 3, 44) (dual of [(21, 3), 16, 45]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(9⁴⁷, 28, F₉, 3, 44) (dual of [(28, 3), 37, 45]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,39P) [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(3²²⁰, 84, F₃, 3, 133) (dual of [(84, 3), 32, 134]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(3²²⁰, 84, F₃, 3, 132) (dual of [(84, 3), 32, 133]-NRT-code)	[i]		Strength Reduction for OOAs
3	Linear OOA(3²²¹, 84, F₃, 3, 134) (dual of [(84, 3), 31, 135]-NRT-code)	[i]		OOA Duplication
4	Linear OOA(3²¹⁹, 83, F₃, 3, 133) (dual of [(83, 3), 30, 134]-NRT-code)	[i]		Truncation for OOAs
5	Linear OOA(3²¹⁸, 83, F₃, 3, 132) (dual of [(83, 3), 31, 133]-NRT-code)	[i]
6	Linear OOA(3²¹⁷, 83, F₃, 3, 131) (dual of [(83, 3), 32, 132]-NRT-code)	[i]
7	Linear OOA(3²¹⁶, 82, F₃, 3, 130) (dual of [(82, 3), 30, 131]-NRT-code)	[i]
8	Linear OOA(3²¹⁵, 82, F₃, 3, 129) (dual of [(82, 3), 31, 130]-NRT-code)	[i]
9	Linear OOA(3²¹⁴, 82, F₃, 3, 128) (dual of [(82, 3), 32, 129]-NRT-code)	[i]
10	Linear OOA(3²¹², 81, F₃, 3, 126) (dual of [(81, 3), 31, 127]-NRT-code)	[i]