MinT - Information on Result #1317746

Information on Result #1317746

Linear OA(3⁶⁷, 114, F₃, 26) (dual of [114, 47, 27]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(3⁶⁵, 111, F₃, 26) (dual of [111, 46, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(3⁶⁵, 122, F₃, 26) (dual of [122, 57, 27]-code), using
  - constructionÂ X with VarÅ¡amov bound [i] based on
    1. linear OA(3⁵⁴, 108, F₃, 26) (dual of [108, 54, 27]-code), using
      - a â€œGraâ€ code from Grasslâ€™s database [i]
    2. linear OA(3⁵⁴, 111, F₃, 19) (dual of [111, 57, 20]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 3⁵⁴Â > V_b^sâˆ’1(kâˆ’1)Â = 57 840743 238250 829997 857529 [i]
    3. linear OA(3⁸, 11, F₃, 6) (dual of [11, 3, 7]-code), using
      - 2 times truncation [i] based on linear OA(3¹⁰, 13, F₃, 8) (dual of [13, 3, 9]-code), using
        Simplex code S(3,3) [i]
        the expurgated narrow-sense BCH-code C(I) with length 13Â | 3³âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−1,0,…,6}|+1Â =Â 9 (BCH-bound) [i]
linear OA(3⁶⁵, 112, F₃, 24) (dual of [112, 47, 25]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 3⁶⁵Â > V_b^sâˆ’1(kâˆ’1)Â = 3 537649 149343 002372 000653 545707 [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, using
  - parity-check code [i]

Mode: Linear.

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