MinT - Information on Result #1030642

Information on Result #1030642

Linear OOA(3²⁰⁸, 76, F₃, 3, 137) (dual of [(76, 3), 20, 138]-NRT-code), using concatenation of two NRT-codes based on

linear OOA(9⁴⁷, 19, F₉, 3, 45) (dual of [(19, 3), 10, 46]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(9⁴⁷, 20, F₉, 3, 45) (dual of [(20, 3), 13, 46]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,14P) [i] based on function field F/F₉ with g(F) = 2 and N(F) ≥ 20, 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(3²⁰⁸, 76, F₃, 3, 136) (dual of [(76, 3), 20, 137]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(3²⁰⁸, 76, F₃, 3, 135) (dual of [(76, 3), 20, 136]-NRT-code)	[i]
3	Linear OOA(3²⁰⁸, 76, F₃, 3, 134) (dual of [(76, 3), 20, 135]-NRT-code)	[i]
4	Linear OOA(3²⁰⁸, 76, F₃, 3, 133) (dual of [(76, 3), 20, 134]-NRT-code)	[i]
5	Linear OOA(3²⁰⁹, 76, F₃, 3, 137) (dual of [(76, 3), 19, 138]-NRT-code)	[i]		OOA Duplication
6	Linear OOA(3²⁰⁶, 75, F₃, 3, 135) (dual of [(75, 3), 19, 136]-NRT-code)	[i]		Truncation for OOAs
7	Linear OOA(3²⁰⁵, 75, F₃, 3, 134) (dual of [(75, 3), 20, 135]-NRT-code)	[i]
8	Linear OOA(3²⁰³, 74, F₃, 3, 132) (dual of [(74, 3), 19, 133]-NRT-code)	[i]
9	Linear OOA(3²⁰², 74, F₃, 3, 131) (dual of [(74, 3), 20, 132]-NRT-code)	[i]
10	Linear OOA(3¹⁹⁹, 73, F₃, 3, 128) (dual of [(73, 3), 20, 129]-NRT-code)	[i]