MinT - Information on Result #2490098

Information on Result #2490098

Linear OOA(3¹⁸³, 172, F₃, 2, 61) (dual of [(172, 2), 161, 62]-NRT-code), using 3¹ times duplication based on linear OOA(3¹⁸², 172, F₃, 2, 61) (dual of [(172, 2), 162, 62]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(27³², 43, F₂₇, 2, 30) (dual of [(43, 2), 54, 31]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(27³², 48, F₂₇, 2, 30) (dual of [(48, 2), 64, 31]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,65P) [i] based on function field F/F₂₇ with g(F) = 2 and N(F) ≥ 48, using
      - a function field by GarcÃa and Quoos [i]
2. linear OA(3¹, 4, F₃, 1) (dual of [4, 3, 2]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹, s, F₃, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
    - parity-check code [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.