MinT - Information on Result #1297953

Information on Result #1297953

Linear OA(3⁵², 129, F₃, 17) (dual of [129, 77, 18]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(3⁵¹, 127, F₃, 17) (dual of [127, 76, 18]-code), using
- constructionÂ X applied to C_e(16) âŠ‚ C_e(15) [i] based on
  1. linear OA(3⁵¹, 122, F₃, 17) (dual of [122, 71, 18]-code), using an extension C_e(16) of the narrow-sense BCH-code C(I) with length 121Â | 3⁵âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
  2. linear OA(3⁴⁶, 122, F₃, 16) (dual of [122, 76, 17]-code), using an extension C_e(15) of the narrow-sense BCH-code C(I) with length 121Â | 3⁵âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
  3. linear OA(3⁰, 5, F₃, 0) (dual of [5, 5, 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(3⁵¹, 128, F₃, 16) (dual of [128, 77, 17]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 3⁵¹Â > V_b^sâˆ’1(kâˆ’1)Â = 409360 130610 578570 815659 [i]
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 (see above)

Mode: Linear.

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