MinT - Information on Result #1298773

Information on Result #1298773

Linear OA(3¹⁶⁶, 191, F₃, 81) (dual of [191, 25, 82]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(3¹⁵⁷, 178, F₃, 81) (dual of [178, 21, 82]-code), using
- 2 times truncation [i] based on linear OA(3¹⁵⁹, 180, F₃, 83) (dual of [180, 21, 84]-code), using
  - concatenation of two codes [i] based on
    1. linear OA(27¹³, 20, F₂₇, 13) (dual of [20, 7, 14]-code or 20-arc in PG(12,27)), using
      - discarding factors / shortening the dual code based on linear OA(27¹³, 27, F₂₇, 13) (dual of [27, 14, 14]-code or 27-arc in PG(12,27)), using
        Reedâ€“Solomon code RS(14,27) [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(3¹⁵⁷, 182, F₃, 76) (dual of [182, 25, 77]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 3¹⁵⁷Â > V_b^sâˆ’1(kâˆ’1)Â = 739 071260 126414 038245 995027 372045 691304 033507 794636 907371 987604 917860 521011 [i]
linear OA(3⁵, 9, F₃, 4) (dual of [9, 4, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(3⁵, 11, F₃, 4) (dual of [11, 6, 5]-code), using
  - Golay code G(3) [i]

Mode: Linear.

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