MinT - Information on Result #2776343

Information on Result #2776343

Linear OOA(3²³², 72, F₃, 4, 132) (dual of [(72, 4), 56, 133]-NRT-code), using strength reduction based on linear OOA(3²³², 72, F₃, 4, 133) (dual of [(72, 4), 56, 134]-NRT-code), using

generalized (u,Â u+v)-construction [i] based on
1. linear OOA(3⁵⁷, 24, F₃, 4, 44) (dual of [(24, 4), 39, 45]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(4;F,51P) [i] based on function field F/F₃ with g(F) = 13 and N(F) ≥ 24, using
    - a function field by SÃ©mirat [i]
2. linear OOA(3⁷⁹, 24, F₃, 4, 66) (dual of [(24, 4), 17, 67]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(4;F,29P) [i] based on function field F/F₃ with g(F) = 13 and N(F) ≥ 24 (see above)
3. linear OOA(3⁹⁶, 24, F₃, 4, 96) (dual of [(24, 4), 0, 97]-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(3²³⁶, 73, F₃, 4, 132) (dual of [(73, 4), 56, 133]-NRT-code)	[i]		NRT-Code Embedding in Larger Space