MinT - Information on Result #2622741

Information on Result #2622741

Linear OOA(3¹³⁸, 57, F₃, 3, 76) (dual of [(57, 3), 33, 77]-NRT-code), using strength reduction based on linear OOA(3¹³⁸, 57, F₃, 3, 77) (dual of [(57, 3), 33, 78]-NRT-code), using

generalized (u,Â u+v)-construction [i] based on
1. linear OOA(3³⁴, 19, F₃, 3, 25) (dual of [(19, 3), 23, 26]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,31P) [i] based on function field F/F₃ with g(F) = 9 and N(F) ≥ 19, using
    - an explicitly constructive algebraic function field [i]
2. linear OOA(3⁴⁷, 19, F₃, 3, 38) (dual of [(19, 3), 10, 39]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,18P) [i] based on function field F/F₃ with g(F) = 9 and N(F) ≥ 19 (see above)
3. linear OOA(3⁵⁷, 19, F₃, 3, 57) (dual of [(19, 3), 0, 58]-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

None.