MinT - Information on Result #2777039

Information on Result #2777039

Linear OOA(3²⁴¹, 81, F₃, 4, 124) (dual of [(81, 4), 83, 125]-NRT-code), using strength reduction based on linear OOA(3²⁴¹, 81, F₃, 4, 125) (dual of [(81, 4), 83, 126]-NRT-code), using

generalized (u,Â u+v)-construction [i] based on
1. linear OOA(3⁵⁶, 27, F₃, 4, 41) (dual of [(27, 4), 52, 42]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(3⁵⁶, 28, F₃, 4, 41) (dual of [(28, 4), 56, 42]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(4;F,70P) [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(3⁷⁷, 27, F₃, 4, 62) (dual of [(27, 4), 31, 63]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(3⁷⁷, 28, F₃, 4, 62) (dual of [(28, 4), 35, 63]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(4;F,49P) [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28 (see above)
3. linear OOA(3¹⁰⁸, 27, F₃, 4, 108) (dual of [(27, 4), 0, 109]-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(3²⁴², 81, F₃, 4, 124) (dual of [(81, 4), 82, 125]-NRT-code)	[i]		OOA Duplication