MinT - Information on Result #907757

Information on Result #907757

Linear OOA(3¹²⁷, 66, F₃, 2, 87) (dual of [(66, 2), 5, 88]-NRT-code), using repeating each code word 2 times based on linear OOA(3⁶¹, 33, F₃, 2, 43) (dual of [(33, 2), 5, 44]-NRT-code), using

generalized (u,Â u+v)-construction [i] based on
1. linear OOA(3¹⁸, 11, F₃, 2, 14) (dual of [(11, 2), 4, 15]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(3¹⁸, 12, F₃, 2, 14) (dual of [(12, 2), 6, 15]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,9P) [i] based on function field F/F₃ with g(F) = 4 and N(F) ≥ 12, using
      - an explicitly constructive algebraic function field [i]
2. linear OOA(3²¹, 11, F₃, 2, 21) (dual of [(11, 2), 1, 22]-NRT-code), using
  - dual of repetition NRT-code with length 11 [i]
3. linear OOA(3²², 11, F₃, 2, 22) (dual of [(11, 2), 0, 23]-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		This result only	Method
1	Linear OOA(3¹⁴¹, 73, F₃, 2, 96) (dual of [(73, 2), 5, 97]-NRT-code)	[i]		Juxtaposition for OOAs