MinT - Information on Result #953819

Information on Result #953819

Linear OOA(3¹²¹, 257, F₃, 3, 28) (dual of [(257, 3), 650, 29]-NRT-code), using OOA 3-folding based on linear OA(3¹²¹, 771, F₃, 28) (dual of [771, 650, 29]-code), using

discarding factors / shortening the dual code based on linear OA(3¹²¹, 772, F₃, 28) (dual of [772, 651, 29]-code), using
- constructionÂ XX applied to C₁Â =Â C([722,18]), C₂Â =Â C([0,21]), C₃Â =Â C₁Â +Â C₂Â =Â C([0,18]), and C_âˆ©Â =Â C₁Â âˆ©Â C₂Â =Â C([722,21]) [i] based on
  1. linear OA(3⁹⁷, 728, F₃, 25) (dual of [728, 631, 26]-code), using the primitive BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â {−6,−5,…,18}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
  2. linear OA(3⁸⁵, 728, F₃, 22) (dual of [728, 643, 23]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â [0,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
  3. linear OA(3¹⁰⁹, 728, F₃, 28) (dual of [728, 619, 29]-code), using the primitive BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â {−6,−5,…,21}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
  4. linear OA(3⁷³, 728, F₃, 19) (dual of [728, 655, 20]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â [0,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]
  5. 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]
  6. linear OA(3⁴, 16, F₃, 2) (dual of [16, 12, 3]-code), using
    - discarding factors / shortening the dual code based on linear OA(3⁴, 40, F₃, 2) (dual of [40, 36, 3]-code), using
      - Hamming code H(4,3) [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.