MinT - Information on Result #2628257

Information on Result #2628257

Linear OOA(3²³⁶, 84, F₃, 3, 163) (dual of [(84, 3), 16, 164]-NRT-code), using strength reduction based on linear OOA(3²³⁶, 84, F₃, 3, 164) (dual of [(84, 3), 16, 165]-NRT-code), using

generalized (u,Â u+v)-construction [i] based on
1. linear OOA(3⁶⁹, 28, F₃, 3, 54) (dual of [(28, 3), 15, 55]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,29P) [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28, using
    - an explicitly constructive algebraic function field [i]
2. linear OOA(3⁸³, 28, F₃, 3, 82) (dual of [(28, 3), 1, 83]-NRT-code), using
  - strength reduction [i] based on linear OOA(3⁸³, 28, F₃, 3, 83) (dual of [(28, 3), 1, 84]-NRT-code), using
    - dual of repetition NRT-code with length 28 [i]
3. linear OOA(3⁸⁴, 28, F₃, 3, 84) (dual of [(28, 3), 0, 85]-NRT-code), using
  - complete OOA / dual of NRT-code with only one code word [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		Method
1	Linear OOA(3²³⁹, 85, F₃, 3, 163) (dual of [(85, 3), 16, 164]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(3²³⁵, 83, F₃, 3, 162) (dual of [(83, 3), 14, 163]-NRT-code)	[i]	Truncation for OOAs
3	Linear OOA(3²³⁴, 83, F₃, 3, 161) (dual of [(83, 3), 15, 162]-NRT-code)	[i]
4	Linear OOA(3²³³, 83, F₃, 3, 160) (dual of [(83, 3), 16, 161]-NRT-code)	[i]
5	Linear OOA(3²³², 82, F₃, 3, 159) (dual of [(82, 3), 14, 160]-NRT-code)	[i]
6	Linear OOA(3²³¹, 82, F₃, 3, 158) (dual of [(82, 3), 15, 159]-NRT-code)	[i]
7	Linear OOA(3²³⁰, 82, F₃, 3, 157) (dual of [(82, 3), 16, 158]-NRT-code)	[i]
8	Linear OOA(3²²⁷, 81, F₃, 3, 154) (dual of [(81, 3), 16, 155]-NRT-code)	[i]