MinT - Information on Result #2235137

Information on Result #2235137

Linear OA(3²⁴¹, 768, F₃, 60) (dual of [768, 527, 61]-code), using 1 times truncation based on linear OA(3²⁴², 769, F₃, 61) (dual of [769, 527, 62]-code), using

constructionÂ XX applied to C₁Â =Â C([307,363]), C₂Â =Â C([313,367]), C₃Â =Â C₁Â +Â C₂Â =Â C([313,363]), and C_âˆ©Â =Â C₁Â âˆ©Â C₂Â =Â C([307,367]) [i] based on
1. linear OA(3²¹⁶, 728, F₃, 57) (dual of [728, 512, 58]-code), using the primitive BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â {307,308,…,363}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 58 [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 {313,314,…,367}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 56 [i]
3. linear OA(3²²⁹, 728, F₃, 61) (dual of [728, 499, 62]-code), using the primitive BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â {307,308,…,367}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 62 [i]
4. linear OA(3²⁰¹, 728, F₃, 51) (dual of [728, 527, 52]-code), using the primitive BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â {313,314,…,363}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 52 [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, 18, F₃, 3) (dual of [18, 13, 4]-code or 18-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		Method
1	Linear OOA(3²⁴¹, 384, F₃, 2, 60) (dual of [(384, 2), 527, 61]-NRT-code)	[i]	OOA Folding
2	Linear OOA(3²⁴¹, 256, F₃, 3, 60) (dual of [(256, 3), 527, 61]-NRT-code)	[i]
3	Linear OOA(3²⁴¹, 192, F₃, 4, 60) (dual of [(192, 4), 527, 61]-NRT-code)	[i]