MinT - Information on Result #816455

Information on Result #816455

Linear OOA(3¹⁴⁰, 143, F₃, 2, 42) (dual of [(143, 2), 146, 43]-NRT-code), using OOA 2-folding based on linear OA(3¹⁴⁰, 286, F₃, 42) (dual of [286, 146, 43]-code), using

1 times code embedding in larger space [i] based on linear OA(3¹³⁹, 285, F₃, 42) (dual of [285, 146, 43]-code), using
- constructionÂ XX applied to C₁Â =Â C([84,121]), C₂Â =Â C([90,125]), C₃Â =Â C₁Â +Â C₂Â =Â C([90,121]), and C_âˆ©Â =Â C₁Â âˆ©Â C₂Â =Â C([84,125]) [i] based on
  1. linear OA(3¹¹¹, 242, F₃, 38) (dual of [242, 131, 39]-code), using the primitive BCH-code C(I) with length 242Â = 3⁵âˆ’1, defining interval IÂ =Â {84,85,…,121}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 39 [i]
  2. linear OA(3¹¹¹, 242, F₃, 36) (dual of [242, 131, 37]-code), using the primitive BCH-code C(I) with length 242Â = 3⁵âˆ’1, defining interval IÂ =Â {90,91,…,125}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 37 [i]
  3. linear OA(3¹²⁶, 242, F₃, 42) (dual of [242, 116, 43]-code), using the primitive BCH-code C(I) with length 242Â = 3⁵âˆ’1, defining interval IÂ =Â {84,85,…,125}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 43 [i]
  4. linear OA(3⁹⁶, 242, F₃, 32) (dual of [242, 146, 33]-code), using the primitive BCH-code C(I) with length 242Â = 3⁵âˆ’1, defining interval IÂ =Â {90,91,…,121}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 33 [i]
  5. linear OA(3⁸, 23, F₃, 5) (dual of [23, 15, 6]-code), using
    - discarding factors / shortening the dual code based on linear OA(3⁸, 26, F₃, 5) (dual of [26, 18, 6]-code), using
      - dual code (with bound on d by constructionÂ Y1) [i] based on
        linear OA(3¹⁸, 26, F₃, 12) (dual of [26, 8, 13]-code), using
        2 times truncation [i] based on 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]
        nonexistence of linear OA(3¹⁷, 21, F₃, 12) (dual of [21, 4, 13]-code), because
        â€œHNâ€ bound on codes from Brouwerâ€™s database [i]
  6. linear OA(3⁵, 20, F₃, 3) (dual of [20, 15, 4]-code or 20-cap in PG(4,3)), using
    - doubling the cap [i] based on linear OA(3⁴, 10, F₃, 3) (dual of [10, 6, 4]-code or 10-cap in PG(3,3)), using
      - ovoid in PG(3,Â 3) [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.