MinT - Information on Result #1298722

Information on Result #1298722

Linear OA(3¹⁵⁴, 177, F₃, 76) (dual of [177, 23, 77]-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, 173, F₃, 73) (dual of [173, 23, 74]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 3¹⁵⁰Â > V_b^sâˆ’1(kâˆ’1)Â = 272203 130876 437500 356148 088609 178686 773985 064087 300580 684130 017775 996017 [i]
linear OA(3², 4, F₃, 2) (dual of [4, 2, 3]-code or 4-arc in PG(1,3)), using
- extended Reedâ€“Solomon code RS_e(2,3) [i]
- Hamming code H(2,3) [i]
- Simplex code S(2,3) [i]
- the Tetracode [i]

Mode: Linear.

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