MinT - Information on Result #916100

Information on Result #916100

Linear OOA(3²⁰², 124, F₃, 2, 104) (dual of [(124, 2), 46, 105]-NRT-code), using concatenation of two NRT-codes based on

linear OOA(9³⁹, 31, F₉, 2, 34) (dual of [(31, 2), 23, 35]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(9³⁹, 32, F₉, 2, 34) (dual of [(32, 2), 25, 35]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,29P) [i] based on function field F/F₉ with g(F) = 5 and N(F) ≥ 32, 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(3²⁰², 124, F₃, 2, 103) (dual of [(124, 2), 46, 104]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(3²⁰², 124, F₃, 2, 102) (dual of [(124, 2), 46, 103]-NRT-code)	[i]		Strength Reduction for OOAs
3	Linear OOA(3²⁰³, 124, F₃, 2, 104) (dual of [(124, 2), 45, 105]-NRT-code)	[i]		OOA Duplication
4	Linear OOA(3²⁰¹, 123, F₃, 2, 103) (dual of [(123, 2), 45, 104]-NRT-code)	[i]		Truncation for OOAs
5	Linear OOA(3²⁰⁰, 123, F₃, 2, 102) (dual of [(123, 2), 46, 103]-NRT-code)	[i]
6	Linear OOA(3¹⁹⁹, 122, F₃, 2, 101) (dual of [(122, 2), 45, 102]-NRT-code)	[i]
7	Linear OOA(3¹⁹⁸, 122, F₃, 2, 100) (dual of [(122, 2), 46, 101]-NRT-code)	[i]
8	Linear OOA(3¹⁹⁷, 121, F₃, 2, 99) (dual of [(121, 2), 45, 100]-NRT-code)	[i]
9	Linear OOA(3²⁰², 62, F₃, 4, 104) (dual of [(62, 4), 46, 105]-NRT-code)	[i]		OOA Folding