MinT - Information on Result #1301423

Information on Result #1301423

Linear OA(5⁶⁵, 82, F₅, 38) (dual of [82, 17, 39]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(5⁶⁴, 80, F₅, 38) (dual of [80, 16, 39]-code), using
- concatenation of two codes [i] based on
  1. linear OA(25¹², 20, F₂₅, 12) (dual of [20, 8, 13]-code or 20-arc in PG(11,25)), using
    - discarding factors / shortening the dual code based on linear OA(25¹², 25, F₂₅, 12) (dual of [25, 13, 13]-code or 25-arc in PG(11,25)), using
      - Reedâ€“Solomon code RS(13,25) [i]
  2. linear OA(5², 4, F₅, 2) (dual of [4, 2, 3]-code or 4-arc in PG(1,5)), using
    - discarding factors / shortening the dual code based on linear OA(5², 5, F₅, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,5)), using
      - Reedâ€“Solomon code RS(3,5) [i]
linear OA(5⁶⁴, 81, F₅, 37) (dual of [81, 17, 38]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 5⁶⁴Â > V_b^sâˆ’1(kâˆ’1)Â = 425 978290 833311 152099 625521 977139 974522 588865 [i]
linear OA(5⁰, 1, F₅, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(5⁰, s, F₅, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
  - OA with only one run / dual of code without redundancy [i]

Mode: Linear.

None.

None.