MinT - Information on Result #1298936

Information on Result #1298936

Linear OA(3¹⁸³, 216, F₃, 88) (dual of [216, 33, 89]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(3¹⁷⁸, 210, F₃, 88) (dual of [210, 32, 89]-code), using
- 34 times truncation [i] based on linear OA(3²¹², 244, F₃, 122) (dual of [244, 32, 123]-code), using
  - constructionÂ X applied to C_e(121) âŠ‚ C_e(120) [i] based on
    1. linear OA(3²¹², 243, F₃, 122) (dual of [243, 31, 123]-code), using an extension C_e(121) of the primitive narrow-sense BCH-code C(I) with length 242Â = 3⁵âˆ’1, defining interval IÂ =Â [1,121], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 122 [i]
    2. linear OA(3²¹¹, 243, F₃, 121) (dual of [243, 32, 122]-code), using an extension C_e(120) of the primitive narrow-sense BCH-code C(I) with length 242Â = 3⁵âˆ’1, defining interval IÂ =Â [1,120], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 121 [i]
    3. linear OA(3⁰, 1, F₃, 0) (dual of [1, 1, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(3⁰, s, F₃, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]
linear OA(3¹⁷⁸, 211, F₃, 83) (dual of [211, 33, 84]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 3¹⁷⁸Â > V_b^sâˆ’1(kâˆ’1)Â = 4 075304 231777 232832 113321 996615 615835 127097 802640 116190 665727 360963 960113 740520 439881 [i]
linear OA(3⁴, 5, F₃, 4) (dual of [5, 1, 5]-code or 5-arc in PG(3,3)), using
- dual of repetition code with length 5 [i]

Mode: Linear.

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