MinT - Information on Result #2277600

Information on Result #2277600

Linear OA(5⁵⁵, 79, F₅, 29) (dual of [79, 24, 30]-code), using 1 times code embedding in larger space based on linear OA(5⁵⁴, 78, F₅, 29) (dual of [78, 24, 30]-code), using

concatenation of two codes [i] based on
1. linear OA(25¹⁴, 26, F₂₅, 14) (dual of [26, 12, 15]-code or 26-arc in PG(13,25)), using
  - extended Reedâ€“Solomon code RS_e(12,25) [i]
  - algebraic-geometric code AG(F, Q+4P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26, using the rational function field F₂₅(x) [i]
  - algebraic-geometric code AG(F, Q+3P) with degQ = 2 and degPÂ =Â 3 [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26 (see above)
2. linear OA(5¹, 3, F₅, 1) (dual of [3, 2, 2]-code), using
  - discarding factors / shortening the dual code based on linear OA(5¹, s, F₅, 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.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

None.