MinT - Information on Result #2266951

Information on Result #2266951

Linear OA(3¹⁴⁰, 282, F₃, 43) (dual of [282, 142, 44]-code), using 1 times code embedding in larger space based on linear OA(3¹³⁹, 281, F₃, 43) (dual of [281, 142, 44]-code), using

constructionÂ XX applied to C₁Â =Â C([82,120]), C₂Â =Â C([88,124]), C₃Â =Â C₁Â +Â C₂Â =Â C([88,120]), and C_âˆ©Â =Â C₁Â âˆ©Â C₂Â =Â C([82,124]) [i] based on
1. linear OA(3¹¹⁵, 242, F₃, 39) (dual of [242, 127, 40]-code), using the primitive BCH-code C(I) with length 242Â = 3⁵âˆ’1, defining interval IÂ =Â {82,83,…,120}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 40 [i]
2. 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]
3. 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]
4. linear OA(3¹⁰⁰, 242, F₃, 33) (dual of [242, 142, 34]-code), using the primitive BCH-code C(I) with length 242Â = 3⁵âˆ’1, defining interval IÂ =Â {88,89,…,120}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 34 [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
      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(3⁵, 16, F₃, 3) (dual of [16, 11, 4]-code or 16-cap in PG(4,3)), using
  - discarding factors / shortening the dual code based on 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

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3¹⁴⁰, 141, F₃, 2, 43) (dual of [(141, 2), 142, 44]-NRT-code)	[i]		OOA Folding
2	Linear OOA(3¹⁴⁰, 94, F₃, 3, 43) (dual of [(94, 3), 142, 44]-NRT-code)	[i]		OOA Folding