MinT - Information on Result #1061608

Information on Result #1061608

Linear OOA(3²⁴⁸, 398597, F₃, 4, 28) (dual of [(398597, 4), 1594140, 29]-NRT-code), using OOA 4-folding based on linear OA(3²⁴⁸, 1594388, F₃, 28) (dual of [1594388, 1594140, 29]-code), using

constructionÂ X applied to C_e(27) âŠ‚ C_e(21) [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(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(3¹³, 65, F₃, 5) (dual of [65, 52, 6]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹³, 80, F₃, 5) (dual of [80, 67, 6]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 80Â = 3⁴âˆ’1, defining interval IÂ =Â [0,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [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(3²⁴⁸, 398597, F₃, 4, 27) (dual of [(398597, 4), 1594140, 28]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(3²⁴⁹, 398597, F₃, 4, 28) (dual of [(398597, 4), 1594139, 29]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(3²⁵⁰, 398597, F₃, 4, 28) (dual of [(398597, 4), 1594138, 29]-NRT-code)	[i]	OOA Duplication
4	Linear OOA(3²⁴⁸, 398597, F₃, 5, 28) (dual of [(398597, 5), 1992737, 29]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
5	Digital (220, 248, 398597)-net over F₃	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound