MinT - Information on Result #2799290

Information on Result #2799290

Linear OOA(3²⁴¹, 398588, F₃, 4, 28) (dual of [(398588, 4), 1594111, 29]-NRT-code), using 3² times duplication based on linear OOA(3²³⁹, 398588, F₃, 4, 28) (dual of [(398588, 4), 1594113, 29]-NRT-code), using

OOA 4-folding [i] based on linear OA(3²³⁹, 1594352, F₃, 28) (dual of [1594352, 1594113, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(3²³⁹, 1594353, F₃, 28) (dual of [1594353, 1594114, 29]-code), using
  - constructionÂ X applied to C_e(27) âŠ‚ C_e(24) [i] based on
    1. linear OA(3²³⁵, 1594323, F₃, 28) (dual of [1594323, 1594088, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 1594322Â = 3¹³âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
    2. linear OA(3²⁰⁹, 1594323, F₃, 25) (dual of [1594323, 1594114, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 1594322Â = 3¹³âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
    3. linear OA(3⁴, 30, F₃, 2) (dual of [30, 26, 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(3²⁴¹, 388888, F₃, 5, 28) (dual of [(388888, 5), 1944199, 29]-NRT-code)	[i]		Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Digital (213, 241, 388888)-net over F₃	[i]		Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound