MinT - Information on Result #2235169

Information on Result #2235169

Linear OA(3²⁴⁹, 784, F₃, 60) (dual of [784, 535, 61]-code), using 1 times truncation based on linear OA(3²⁵⁰, 785, F₃, 61) (dual of [785, 535, 62]-code), using

constructionÂ XX applied to C₁Â =Â C([337,391]), C₂Â =Â C([331,385]), C₃Â =Â C₁Â +Â C₂Â =Â C([337,385]), and C_âˆ©Â =Â C₁Â âˆ©Â C₂Â =Â C([331,391]) [i] based on
1. linear OA(3²¹¹, 728, F₃, 55) (dual of [728, 517, 56]-code), using the primitive BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â {337,338,…,391}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 56 [i]
2. linear OA(3²¹⁴, 728, F₃, 55) (dual of [728, 514, 56]-code), using the primitive BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â {331,332,…,385}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 56 [i]
3. linear OA(3²³², 728, F₃, 61) (dual of [728, 496, 62]-code), using the primitive BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â {331,332,…,391}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 62 [i]
4. linear OA(3¹⁹³, 728, F₃, 49) (dual of [728, 535, 50]-code), using the primitive BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â {337,338,…,385}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 50 [i]
5. 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
    1. 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]
    2. 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(3¹⁰, 31, F₃, 5) (dual of [31, 21, 6]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁰, 36, F₃, 5) (dual of [36, 26, 6]-code), using
    - (u,Â uâˆ’v,Â u+v+w)-construction [i] based on
      1. linear OA(3¹, 12, F₃, 1) (dual of [12, 11, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(3¹, s, F₃, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
      2. linear OA(3³, 12, F₃, 2) (dual of [12, 9, 3]-code), using
        discarding factors / shortening the dual code based on linear OA(3³, 13, F₃, 2) (dual of [13, 10, 3]-code), using
        Hamming code H(3,3) [i]
      3. linear OA(3⁶, 12, F₃, 5) (dual of [12, 6, 6]-code), using
        extended Golay code G_e(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

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3²⁴⁹, 392, F₃, 2, 60) (dual of [(392, 2), 535, 61]-NRT-code)	[i]		OOA Folding