MinT - Information on Result #893861

Information on Result #893861

Linear OOA(3²³⁶, 4783002, F₃, 2, 18) (dual of [(4783002, 2), 9565768, 19]-NRT-code), using trace code based on linear OOA(9¹¹⁸, 2391501, F₉, 2, 18) (dual of [(2391501, 2), 4782884, 19]-NRT-code), using

OOA 2-folding [i] based on linear OA(9¹¹⁸, 4783002, F₉, 18) (dual of [4783002, 4782884, 19]-code), using
- 1 times truncation [i] based on linear OA(9¹¹⁹, 4783003, F₉, 19) (dual of [4783003, 4782884, 20]-code), using
  - constructionÂ X applied to C_e(18) âŠ‚ C_e(13) [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(9⁸⁵, 4782969, F₉, 14) (dual of [4782969, 4782884, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
    3. linear OA(9⁶, 34, F₉, 4) (dual of [34, 28, 5]-code), using
      - discarding factors / shortening the dual code based on linear OA(9⁶, 72, F₉, 4) (dual of [72, 66, 5]-code), using
        1 times truncation [i] 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		This result only	Method
1	Linear OOA(3²³⁷, 4783002, F₃, 2, 18) (dual of [(4783002, 2), 9565767, 19]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(3²³⁶, 2391501, F₃, 4, 18) (dual of [(2391501, 4), 9565768, 19]-NRT-code)	[i]		OOA Folding