MinT - Information on Result #916055

Information on Result #916055

Linear OOA(3¹⁶⁸, 100, F₃, 2, 95) (dual of [(100, 2), 32, 96]-NRT-code), using concatenation of two NRT-codes based on

linear OOA(9³⁴, 25, F₉, 2, 31) (dual of [(25, 2), 16, 32]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(9³⁴, 28, F₉, 2, 31) (dual of [(28, 2), 22, 32]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,24P) [i] based on function field F/F₉ with g(F) = 3 and N(F) ≥ 28, using
    - the Hermitian function field over F₉ [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(3¹⁶⁸, 100, F₃, 2, 94) (dual of [(100, 2), 32, 95]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(3¹⁶⁸, 100, F₃, 2, 93) (dual of [(100, 2), 32, 94]-NRT-code)	[i]		Strength Reduction for OOAs
3	Linear OOA(3¹⁶⁹, 100, F₃, 2, 95) (dual of [(100, 2), 31, 96]-NRT-code)	[i]		OOA Duplication
4	Linear OOA(3¹⁶⁷, 99, F₃, 2, 94) (dual of [(99, 2), 31, 95]-NRT-code)	[i]		Truncation for OOAs
5	Linear OOA(3¹⁶⁶, 99, F₃, 2, 93) (dual of [(99, 2), 32, 94]-NRT-code)	[i]
6	Linear OOA(3¹⁶⁵, 98, F₃, 2, 92) (dual of [(98, 2), 31, 93]-NRT-code)	[i]
7	Linear OOA(3¹⁶⁴, 98, F₃, 2, 91) (dual of [(98, 2), 32, 92]-NRT-code)	[i]
8	Linear OOA(3¹⁶³, 97, F₃, 2, 90) (dual of [(97, 2), 31, 91]-NRT-code)	[i]
9	Linear OOA(3¹⁶², 97, F₃, 2, 89) (dual of [(97, 2), 32, 90]-NRT-code)	[i]
10	Linear OOA(3¹⁶¹, 96, F₃, 2, 88) (dual of [(96, 2), 31, 89]-NRT-code)	[i]
11	Linear OOA(3¹⁶⁸, 50, F₃, 4, 95) (dual of [(50, 4), 32, 96]-NRT-code)	[i]		OOA Folding