MinT - Information on Result #2305831

Information on Result #2305831

Linear OA(2¹⁷⁴, 319, F₂, 44) (dual of [319, 145, 45]-code), using 2 times code embedding in larger space based on linear OA(2¹⁷², 317, F₂, 44) (dual of [317, 145, 45]-code), using

1 times truncation [i] based on linear OA(2¹⁷³, 318, F₂, 45) (dual of [318, 145, 46]-code), using
- concatenation of two codes [i] based on
  1. linear OA(32²⁴, 53, F₃₂, 22) (dual of [53, 29, 23]-code), using
    - extended algebraic-geometric code AG_e(F,30P) [i] based on function field F/F₃₂ with g(F) = 2 and N(F) ≥ 53, using
      - sharp bound on the number of rational points on curves with genus 2 [i]
  2. linear OA(2¹, 6, F₂, 1) (dual of [6, 5, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [i]

Mode: 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.