MinT - Information on Result #912284

Information on Result #912284

Linear OOA(3¹⁰⁶, 56, F₃, 2, 76) (dual of [(56, 2), 6, 77]-NRT-code), using concatenation of two NRT-codes based on

linear OA(9¹¹, 14, F₉, 10) (dual of [14, 3, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(9¹¹, 16, F₉, 10) (dual of [16, 5, 11]-code), using
  - extended algebraic-geometric code AG_e(F,5P) [i] based on function field F/F₉ with g(F) = 1 and N(F) ≥ 16, using
    - a function field by GarcÃa and Quoos [i]
linear OOA(3⁶, 4, F₃, 2, 6) (dual of [(4, 2), 2, 7]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(2;2,3) [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(3¹⁰⁶, 56, F₃, 2, 75) (dual of [(56, 2), 6, 76]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(3¹⁰⁶, 56, F₃, 2, 74) (dual of [(56, 2), 6, 75]-NRT-code)	[i]
3	Linear OOA(3¹⁰⁶, 56, F₃, 2, 73) (dual of [(56, 2), 6, 74]-NRT-code)	[i]
4	Linear OOA(3¹⁰⁵, 55, F₃, 2, 75) (dual of [(55, 2), 5, 76]-NRT-code)	[i]		Truncation for OOAs
5	Linear OOA(3¹⁰⁴, 55, F₃, 2, 74) (dual of [(55, 2), 6, 75]-NRT-code)	[i]
6	Linear OOA(3¹⁰³, 54, F₃, 2, 73) (dual of [(54, 2), 5, 74]-NRT-code)	[i]
7	Linear OOA(3¹⁰², 54, F₃, 2, 72) (dual of [(54, 2), 6, 73]-NRT-code)	[i]
8	Linear OOA(3¹⁰¹, 53, F₃, 2, 71) (dual of [(53, 2), 5, 72]-NRT-code)	[i]
9	Linear OOA(3¹⁰⁰, 53, F₃, 2, 70) (dual of [(53, 2), 6, 71]-NRT-code)	[i]
10	Linear OOA(3⁹⁹, 52, F₃, 2, 69) (dual of [(52, 2), 5, 70]-NRT-code)	[i]
11	Linear OOA(3⁹⁶, 51, F₃, 2, 66) (dual of [(51, 2), 6, 67]-NRT-code)	[i]
12	Linear OOA(3¹⁰⁶, 28, F₃, 4, 76) (dual of [(28, 4), 6, 77]-NRT-code)	[i]		OOA Folding