MinT - Information on Result #2487031

Information on Result #2487031

Linear OOA(3²⁰², 88602, F₃, 2, 26) (dual of [(88602, 2), 177002, 27]-NRT-code), using 3¹ times duplication based on linear OOA(3²⁰¹, 88602, F₃, 2, 26) (dual of [(88602, 2), 177003, 27]-NRT-code), using

1 times NRT-code embedding in larger space [i] based on linear OOA(3¹⁹⁹, 88601, F₃, 2, 26) (dual of [(88601, 2), 177003, 27]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3¹⁹⁹, 177202, F₃, 26) (dual of [177202, 177003, 27]-code), using
  - constructionÂ X applied to C_e(25) âŠ‚ C_e(19) [i] based on
    1. linear OA(3¹⁸⁸, 177147, F₃, 26) (dual of [177147, 176959, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
    2. linear OA(3¹⁴⁴, 177147, F₃, 20) (dual of [177147, 177003, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [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(3²⁰², 66399, F₃, 3, 26) (dual of [(66399, 3), 198995, 27]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3²⁰², 66399, F₃, 4, 26) (dual of [(66399, 4), 265394, 27]-NRT-code)	[i]
3	Linear OOA(3²⁰², 66399, F₃, 5, 26) (dual of [(66399, 5), 331793, 27]-NRT-code)	[i]
4	Digital (176, 202, 66399)-net over F₃	[i]