MinT - Information on Result #2486748

Information on Result #2486748

Linear OOA(3¹⁸⁰, 88602, F₃, 2, 23) (dual of [(88602, 2), 177024, 24]-NRT-code), using 3¹ times duplication based on linear OOA(3¹⁷⁹, 88602, F₃, 2, 23) (dual of [(88602, 2), 177025, 24]-NRT-code), using

1 times NRT-code embedding in larger space [i] based on linear OOA(3¹⁷⁷, 88601, F₃, 2, 23) (dual of [(88601, 2), 177025, 24]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3¹⁷⁷, 177202, F₃, 23) (dual of [177202, 177025, 24]-code), using
  - constructionÂ X applied to C_e(22) âŠ‚ C_e(16) [i] based on
    1. linear OA(3¹⁶⁶, 177147, F₃, 23) (dual of [177147, 176981, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
    2. linear OA(3¹²², 177147, F₃, 17) (dual of [177147, 177025, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
    3. linear OA(3¹¹, 55, F₃, 5) (dual of [55, 44, 6]-code), using
      - discarding factors / shortening the dual code based on linear OA(3¹¹, 85, F₃, 5) (dual of [85, 74, 6]-code), using
        codes constructed by inverting constructionÂ Y₁ [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(3¹⁸⁰, 73205, F₃, 3, 23) (dual of [(73205, 3), 219435, 24]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3¹⁸⁰, 73205, F₃, 4, 23) (dual of [(73205, 4), 292640, 24]-NRT-code)	[i]
3	Linear OOA(3¹⁸⁰, 73205, F₃, 5, 23) (dual of [(73205, 5), 365845, 24]-NRT-code)	[i]
4	Digital (157, 180, 73205)-net over F₃	[i]