MinT - Information on Result #1317988

Information on Result #1317988

Linear OA(5³⁸, 56, F₅, 21) (dual of [56, 18, 22]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(5³⁷, 54, F₅, 21) (dual of [54, 17, 22]-code), using
- constructionÂ X with VarÅ¡amov bound [i] based on
  1. linear OA(5³⁵, 51, F₅, 21) (dual of [51, 16, 22]-code), using
    - discarding factors / shortening the dual code based on linear OA(5³⁵, 52, F₅, 21) (dual of [52, 17, 22]-code), using
      - a â€œGraXâ€ code from Grasslâ€™s database [i]
  2. linear OA(5³⁵, 52, F₅, 19) (dual of [52, 17, 20]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 5³⁵Â > V_b^sâˆ’1(kâˆ’1)Â = 2 205720 838209 052417 532605 [i]
  3. linear OA(5¹, 2, F₅, 1) (dual of [2, 1, 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]
linear OA(5³⁷, 55, F₅, 20) (dual of [55, 18, 21]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 5³⁷Â > V_b^sâˆ’1(kâˆ’1)Â = 58 052969 352410 112382 858825 [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.

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