MinT - Information on Result #1298441

Information on Result #1298441

Linear OA(3¹¹⁵, 155, F₃, 49) (dual of [155, 40, 50]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(3¹¹³, 152, F₃, 49) (dual of [152, 39, 50]-code), using
- concatenation of two codes [i] based on
  1. linear OA(27²⁵, 38, F₂₇, 24) (dual of [38, 13, 25]-code), using
    - extended algebraic-geometric code AG_e(F,13P) [i] based on function field F/F₂₇ with g(F) = 1 and N(F) ≥ 38, using
      - a function field by SÃ©mirat [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]
linear OA(3¹¹³, 153, F₃, 47) (dual of [153, 40, 48]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 3¹¹³Â > V_b^sâˆ’1(kâˆ’1)Â = 185935 018259 246096 240157 600257 769977 347528 667334 308577 [i]
linear OA(3¹, 2, F₃, 1) (dual of [2, 1, 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 (see above)

Mode: Linear.

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