MinT - Information on Result #2776989

Information on Result #2776989

Linear OOA(3²⁴⁰, 84, F₃, 4, 118) (dual of [(84, 4), 96, 119]-NRT-code), using strength reduction based on linear OOA(3²⁴⁰, 84, F₃, 4, 119) (dual of [(84, 4), 96, 120]-NRT-code), using

generalized (u,Â u+v)-construction [i] based on
1. linear OOA(3⁵⁴, 28, F₃, 4, 39) (dual of [(28, 4), 58, 40]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(4;F,72P) [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(3⁷⁴, 28, F₃, 4, 59) (dual of [(28, 4), 38, 60]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(4;F,52P) [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28 (see above)
3. linear OOA(3¹¹², 28, F₃, 4, 112) (dual of [(28, 4), 0, 113]-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(3²⁴⁴, 85, F₃, 4, 118) (dual of [(85, 4), 96, 119]-NRT-code)	[i]		NRT-Code Embedding in Larger Space
2	Linear OOA(3²⁴¹, 84, F₃, 4, 118) (dual of [(84, 4), 95, 119]-NRT-code)	[i]		OOA Duplication