MinT - Information on Result #916151

Information on Result #916151

Linear OOA(3²⁰⁸, 116, F₃, 2, 128) (dual of [(116, 2), 24, 129]-NRT-code), using concatenation of two NRT-codes based on

linear OOA(9⁴⁶, 29, F₉, 2, 42) (dual of [(29, 2), 12, 43]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(9⁴⁶, 30, F₉, 2, 42) (dual of [(30, 2), 14, 43]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,17P) [i] based on function field F/F₉ with g(F) = 4 and N(F) ≥ 30, using
    - a function field by SÃ©mirat [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, 116, F₃, 2, 127) (dual of [(116, 2), 24, 128]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(3²⁰⁸, 116, F₃, 2, 126) (dual of [(116, 2), 24, 127]-NRT-code)	[i]		Strength Reduction for OOAs
3	Linear OOA(3²⁰⁹, 116, F₃, 2, 128) (dual of [(116, 2), 23, 129]-NRT-code)	[i]		OOA Duplication
4	Linear OOA(3²⁰⁷, 115, F₃, 2, 127) (dual of [(115, 2), 23, 128]-NRT-code)	[i]		Truncation for OOAs
5	Linear OOA(3²⁰⁶, 115, F₃, 2, 126) (dual of [(115, 2), 24, 127]-NRT-code)	[i]
6	Linear OOA(3²⁰⁵, 114, F₃, 2, 125) (dual of [(114, 2), 23, 126]-NRT-code)	[i]
7	Linear OOA(3²⁰⁴, 114, F₃, 2, 124) (dual of [(114, 2), 24, 125]-NRT-code)	[i]
8	Linear OOA(3²⁰³, 113, F₃, 2, 123) (dual of [(113, 2), 23, 124]-NRT-code)	[i]
9	Linear OOA(3²⁰⁸, 58, F₃, 4, 128) (dual of [(58, 4), 24, 129]-NRT-code)	[i]		OOA Folding