MinT - Information on Result #704648

Information on Result #704648

Linear OA(3¹⁴², 772, F₃, 34) (dual of [772, 630, 35]-code), using constructionÂ XX applied to C₁Â =Â C([334,364]), C₂Â =Â C([340,367]), C₃Â =Â C₁Â +Â C₂Â =Â C([340,364]), and C_âˆ©Â =Â C₁Â âˆ©Â C₂Â =Â C([334,367]) based on

linear OA(3¹¹⁸, 728, F₃, 31) (dual of [728, 610, 32]-code), using the primitive BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â {334,335,…,364}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 32 [i]
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 {340,341,…,367}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
linear OA(3¹³⁰, 728, F₃, 34) (dual of [728, 598, 35]-code), using the primitive BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â {334,335,…,367}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 35 [i]
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 {340,341,…,364}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
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]
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

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3¹⁴², 386, F₃, 2, 34) (dual of [(386, 2), 630, 35]-NRT-code)	[i]		OOA Folding
2	Linear OOA(3¹⁴², 257, F₃, 3, 34) (dual of [(257, 3), 629, 35]-NRT-code)	[i]		OOA Folding