MinT - Information on Result #813751

Information on Result #813751

Linear OOA(3⁷⁸, 135, F₃, 2, 21) (dual of [(135, 2), 192, 22]-NRT-code), using OOA 2-folding based on linear OA(3⁷⁸, 270, F₃, 21) (dual of [270, 192, 22]-code), using

1 times truncation [i] based on linear OA(3⁷⁹, 271, F₃, 22) (dual of [271, 192, 23]-code), using
- constructionÂ X applied to C_e(21) âŠ‚ C_e(15) [i] based on
  1. linear OA(3⁷¹, 243, F₃, 22) (dual of [243, 172, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 242Â = 3⁵âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
  2. linear OA(3⁵¹, 243, F₃, 16) (dual of [243, 192, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 242Â = 3⁵âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
  3. linear OA(3⁸, 28, F₃, 5) (dual of [28, 20, 6]-code), using
    - dual code (with bound on d by constructionÂ Y1) [i] based on
      1. linear OA(3²⁰, 28, F₃, 14) (dual of [28, 8, 15]-code), using
        contraction [i] based on linear OA(3⁴⁸, 56, F₃, 29) (dual of [56, 8, 30]-code), using the BCH-code C(I) with length 56Â | 3⁶âˆ’1, defining interval IÂ =Â {0,1,…,28}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 30 [i]
      2. nonexistence of linear OA(3¹⁹, 23, F₃, 14) (dual of [23, 4, 15]-code), because
        2 times truncation [i] would yield linear OA(3¹⁷, 21, F₃, 12) (dual of [21, 4, 13]-code), but
        â€œHNâ€ bound on codes from Brouwerâ€™s database [i]

Mode: Constructive and 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.