MinT - Information on Result #703590

Information on Result #703590

Linear OA(3¹³⁵, 271, F₃, 43) (dual of [271, 136, 44]-code), using constructionÂ XX applied to C₁Â =Â C([82,122]), C₂Â =Â C([88,124]), C₃Â =Â C₁Â +Â C₂Â =Â C([88,122]), and C_âˆ©Â =Â C₁Â âˆ©Â C₂Â =Â C([82,124]) based on

linear OA(3¹²¹, 242, F₃, 41) (dual of [242, 121, 42]-code), using the primitive BCH-code C(I) with length 242Â = 3⁵âˆ’1, defining interval IÂ =Â {82,83,…,122}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 42 [i]
linear OA(3¹¹¹, 242, F₃, 37) (dual of [242, 131, 38]-code), using the primitive BCH-code C(I) with length 242Â = 3⁵âˆ’1, defining interval IÂ =Â {88,89,…,124}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 38 [i]
linear OA(3¹²⁶, 242, F₃, 43) (dual of [242, 116, 44]-code), using the primitive BCH-code C(I) with length 242Â = 3⁵âˆ’1, defining interval IÂ =Â {82,83,…,124}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 44 [i]
linear OA(3¹⁰⁶, 242, F₃, 35) (dual of [242, 136, 36]-code), using the primitive BCH-code C(I) with length 242Â = 3⁵âˆ’1, defining interval IÂ =Â {88,89,…,122}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 36 [i]
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
    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]
linear OA(3¹, 6, F₃, 1) (dual of [6, 5, 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]

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		Method
1	Linear OA(3¹³⁶, 272, F₃, 43) (dual of [272, 136, 44]-code)	[i]	Code Embedding in Larger Space
2	Linear OOA(3¹³⁵, 135, F₃, 2, 43) (dual of [(135, 2), 135, 44]-NRT-code)	[i]	OOA Folding
3	Linear OOA(3¹³⁵, 90, F₃, 3, 43) (dual of [(90, 3), 135, 44]-NRT-code)	[i]	OOA Folding