MinT - Information on Result #2301112

Information on Result #2301112

Linear OA(3²²⁶, 262, F₃, 110) (dual of [262, 36, 111]-code), using 2 times truncation based on linear OA(3²²⁸, 264, F₃, 112) (dual of [264, 36, 113]-code), using

constructionÂ X with VarÅ¡amov bound [i] based on
1. linear OA(3²⁰², 234, F₃, 112) (dual of [234, 32, 113]-code), using
  - 10 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]
2. linear OA(3²⁰², 238, F₃, 95) (dual of [238, 36, 96]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 3²⁰²Â > V_b^sâˆ’1(kâˆ’1)Â = 2 082283 569496 480370 118370 351257 578751 782258 579744 906929 510067 472046 170251 555226 351611 124071 345235 [i]
3. linear OA(3²², 26, F₃, 16) (dual of [26, 4, 17]-code), using
  - 1 times truncation [i] based on linear OA(3²³, 27, F₃, 17) (dual of [27, 4, 18]-code), using
    - a code of Belov type defined by PG(3,3) ∖ PG(2,3) [i]

Mode: Linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

None.