MinT - Information on Result #1298359

Information on Result #1298359

Linear OA(3¹¹⁹, 144, F₃, 56) (dual of [144, 25, 57]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(3¹⁰¹, 121, F₃, 56) (dual of [121, 20, 57]-code), using
- a cyclic, quasi-cyclic, or quasi-twisted code by Daskalov, Hristov, and Metodieva [i]
linear OA(3¹⁰¹, 126, F₃, 46) (dual of [126, 25, 47]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 3¹⁰¹Â > V_b^sâˆ’1(kâˆ’1)Â = 1 066150 248248 402975 734237 121048 937725 665833 838611 [i]
linear OA(3¹³, 18, F₃, 9) (dual of [18, 5, 10]-code), using
- 2 times truncation [i] based on linear OA(3¹⁵, 20, F₃, 11) (dual of [20, 5, 12]-code), using
  - residual code [i] based on linear OA(3⁵⁰, 56, F₃, 35) (dual of [56, 6, 36]-code), using
    - dual code (with bound on d by constructionÂ Y1) [i] based on
      1. linear OA(3⁶, 56, F₃, 3) (dual of [56, 50, 4]-code or 56-cap in PG(5,3)), using
        the Hill cap [i]
      2. nonexistence of linear OA(3⁵, 21, F₃, 3) (dual of [21, 16, 4]-code or 21-cap in PG(4,3)), because
        20 is the largest size of a cap in PG(4,Â 3) [i]

Mode: Linear.

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