MinT - Information on Result #2677892

Information on Result #2677892

Linear OOA(3²³², 531457, F₃, 3, 26) (dual of [(531457, 3), 1594139, 27]-NRT-code), using 3¹ times duplication based on linear OOA(3²³¹, 531457, F₃, 3, 26) (dual of [(531457, 3), 1594140, 27]-NRT-code), using

1 times NRT-code embedding in larger space [i] based on linear OOA(3²²⁸, 531456, F₃, 3, 26) (dual of [(531456, 3), 1594140, 27]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3²²⁸, 1594368, F₃, 26) (dual of [1594368, 1594140, 27]-code), using
  - constructionÂ X applied to C_e(25) âŠ‚ C_e(21) [i] based on
    1. linear OA(3²²², 1594323, F₃, 26) (dual of [1594323, 1594101, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 1594322Â = 3¹³âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
    2. linear OA(3¹⁸³, 1594323, F₃, 22) (dual of [1594323, 1594140, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 1594322Â = 3¹³âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
    3. linear OA(3⁶, 45, F₃, 3) (dual of [45, 39, 4]-code or 45-cap in PG(5,3)), using
      - discarding factors / shortening the dual code based on linear OA(3⁶, 48, F₃, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
        large caps in PG(5,Â b) [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(3²³², 418986, F₃, 4, 26) (dual of [(418986, 4), 1675712, 27]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3²³², 418986, F₃, 5, 26) (dual of [(418986, 5), 2094698, 27]-NRT-code)	[i]
3	Digital (206, 232, 418986)-net over F₃	[i]