MinT - Information on Result #2677284

Information on Result #2677284

Linear OOA(3¹⁷³, 531446, F₃, 3, 20) (dual of [(531446, 3), 1594165, 21]-NRT-code), using 3¹ times duplication based on linear OOA(3¹⁷², 531446, F₃, 3, 20) (dual of [(531446, 3), 1594166, 21]-NRT-code), using

OOA 3-folding [i] based on linear OA(3¹⁷², 1594338, F₃, 20) (dual of [1594338, 1594166, 21]-code), using
- 2 times code embedding in larger space [i] based on linear OA(3¹⁷⁰, 1594336, F₃, 20) (dual of [1594336, 1594166, 21]-code), using
  - constructionÂ X applied to C_e(19) âŠ‚ C_e(18) [i] based on
    1. linear OA(3¹⁷⁰, 1594323, F₃, 20) (dual of [1594323, 1594153, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 1594322Â = 3¹³âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]
    2. linear OA(3¹⁵⁷, 1594323, F₃, 19) (dual of [1594323, 1594166, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 1594322Â = 3¹³âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
    3. linear OA(3⁰, 13, F₃, 0) (dual of [13, 13, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(3⁰, s, F₃, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [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(3¹⁷³, 398938, F₃, 4, 20) (dual of [(398938, 4), 1595579, 21]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3¹⁷³, 398938, F₃, 5, 20) (dual of [(398938, 5), 1994517, 21]-NRT-code)	[i]
3	Digital (153, 173, 398938)-net over F₃	[i]