MinT - Information on Result #2677581

Information on Result #2677581

Linear OOA(3²⁰⁶, 531457, F₃, 3, 23) (dual of [(531457, 3), 1594165, 24]-NRT-code), using 3¹ times duplication based on linear OOA(3²⁰⁵, 531457, F₃, 3, 23) (dual of [(531457, 3), 1594166, 24]-NRT-code), using

1 times NRT-code embedding in larger space [i] based on linear OOA(3²⁰², 531456, F₃, 3, 23) (dual of [(531456, 3), 1594166, 24]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3²⁰², 1594368, F₃, 23) (dual of [1594368, 1594166, 24]-code), using
  - constructionÂ X applied to C_e(22) âŠ‚ C_e(18) [i] based on
    1. linear OA(3¹⁹⁶, 1594323, F₃, 23) (dual of [1594323, 1594127, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 1594322Â = 3¹³âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [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(3⁶, 45, F₃, 3) (dual of [45, 39, 4]-code or 45-cap in PG(5,3)), using
      - discarding factors / shortening the dual code based on linear OA(3⁶, 48, F₃, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
        large caps in PG(5,Â b) [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(3²⁰⁶, 496402, F₃, 4, 23) (dual of [(496402, 4), 1985402, 24]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3²⁰⁶, 496402, F₃, 5, 23) (dual of [(496402, 5), 2481804, 24]-NRT-code)	[i]
3	Digital (183, 206, 496402)-net over F₃	[i]