MinT - Information on Result #1008765

Information on Result #1008765

Linear OOA(3²³⁸, 3188672, F₃, 3, 18) (dual of [(3188672, 3), 9565778, 19]-NRT-code), using trace code based on linear OOA(9¹¹⁹, 1594336, F₉, 3, 18) (dual of [(1594336, 3), 4782889, 19]-NRT-code), using

OOA 3-folding [i] based on linear OA(9¹¹⁹, 4783008, F₉, 18) (dual of [4783008, 4782889, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(9¹¹⁹, 4783010, F₉, 18) (dual of [4783010, 4782891, 19]-code), using
  - 1 times truncation [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		This result only	Method
1	Linear OOA(3²³⁸, 1062890, F₃, 21, 18) (dual of [(1062890, 21), 22320452, 19]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row