MinT - Information on Result #1298721

Information on Result #1298721

Linear OA(3¹⁵⁴, 176, F₃, 77) (dual of [176, 22, 78]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(3¹⁵⁰, 171, F₃, 77) (dual of [171, 21, 78]-code), using
- concatenation of two codes [i] based on
  1. linear OA(27¹², 19, F₂₇, 12) (dual of [19, 7, 13]-code or 19-arc in PG(11,27)), using
    - discarding factors / shortening the dual code based on linear OA(27¹², 27, F₂₇, 12) (dual of [27, 15, 13]-code or 27-arc in PG(11,27)), using
      - Reedâ€“Solomon code RS(15,27) [i]
  2. linear OA(3⁶, 9, F₃, 5) (dual of [9, 3, 6]-code), using
    - discarding factors / shortening the dual code based on linear OA(3⁶, 10, F₃, 5) (dual of [10, 4, 6]-code), using
      - projective code from ovoid in PG(3,Â 3) [i]
linear OA(3¹⁵⁰, 172, F₃, 73) (dual of [172, 22, 74]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 3¹⁵⁰Â > V_b^sâˆ’1(kâˆ’1)Â = 159101 451781 768872 179005 113740 685519 612123 158874 750822 307801 114139 433339 [i]
linear OA(3³, 4, F₃, 3) (dual of [4, 1, 4]-code or 4-arc in PG(2,3) or 4-cap in PG(2,3)), using
- dual of repetition code with length 4 [i]
- oval in PG(2,Â 3) [i]

Mode: Linear.

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