MinT - Information on Result #916008

Information on Result #916008

Linear OOA(3¹²⁴, 72, F₃, 2, 74) (dual of [(72, 2), 20, 75]-NRT-code), using concatenation of two NRT-codes based on

linear OOA(9²⁶, 18, F₉, 2, 24) (dual of [(18, 2), 10, 25]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(9²⁶, 20, F₉, 2, 24) (dual of [(20, 2), 14, 25]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,15P) [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(3¹²⁴, 72, F₃, 2, 73) (dual of [(72, 2), 20, 74]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(3¹²⁴, 72, F₃, 2, 72) (dual of [(72, 2), 20, 73]-NRT-code)	[i]		Strength Reduction for OOAs
3	Linear OOA(3¹²⁵, 72, F₃, 2, 74) (dual of [(72, 2), 19, 75]-NRT-code)	[i]		OOA Duplication
4	Linear OOA(3¹²³, 71, F₃, 2, 73) (dual of [(71, 2), 19, 74]-NRT-code)	[i]		Truncation for OOAs
5	Linear OOA(3¹²², 71, F₃, 2, 72) (dual of [(71, 2), 20, 73]-NRT-code)	[i]
6	Linear OOA(3¹²¹, 70, F₃, 2, 71) (dual of [(70, 2), 19, 72]-NRT-code)	[i]
7	Linear OOA(3¹²⁰, 70, F₃, 2, 70) (dual of [(70, 2), 20, 71]-NRT-code)	[i]
8	Linear OOA(3¹¹⁹, 69, F₃, 2, 69) (dual of [(69, 2), 19, 70]-NRT-code)	[i]
9	Linear OOA(3¹¹⁸, 69, F₃, 2, 68) (dual of [(69, 2), 20, 69]-NRT-code)	[i]
10	Linear OOA(3¹²⁴, 36, F₃, 4, 74) (dual of [(36, 4), 20, 75]-NRT-code)	[i]		OOA Folding