MinT - Information on Result #893869

Information on Result #893869

Linear OOA(3²⁴², 4783012, F₃, 2, 19) (dual of [(4783012, 2), 9565782, 20]-NRT-code), using trace code based on linear OOA(9¹²¹, 2391506, F₉, 2, 19) (dual of [(2391506, 2), 4782891, 20]-NRT-code), using

OOA 2-folding [i] based on linear OA(9¹²¹, 4783012, F₉, 19) (dual of [4783012, 4782891, 20]-code), using
- 1 times code embedding in larger space [i] based on linear OA(9¹²⁰, 4783011, F₉, 19) (dual of [4783011, 4782891, 20]-code), using
  - constructionÂ X applied to C_e(18) âŠ‚ C_e(12) [i] based on
    1. linear OA(9¹¹³, 4782969, F₉, 19) (dual of [4782969, 4782856, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
    2. linear OA(9⁷⁸, 4782969, F₉, 13) (dual of [4782969, 4782891, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
    3. linear OA(9⁷, 42, F₉, 5) (dual of [42, 35, 6]-code), using
      - discarding factors / shortening the dual code based on linear OA(9⁷, 73, F₉, 5) (dual of [73, 66, 6]-code), using
        a code by Danev and Olsson [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Linear OOA(3²⁴⁴, 4783013, F₃, 2, 19) (dual of [(4783013, 2), 9565782, 20]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(3²⁴⁶, 4783014, F₃, 2, 19) (dual of [(4783014, 2), 9565782, 20]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
3	Linear OOA(3²⁴³, 4783012, F₃, 2, 19) (dual of [(4783012, 2), 9565781, 20]-NRT-code)	[i]	OOA Duplication
4	Linear OOA(3²⁴², 2391506, F₃, 4, 19) (dual of [(2391506, 4), 9565782, 20]-NRT-code)	[i]	OOA Folding