MinT - Information on Result #893870

Information on Result #893870

Linear OOA(3²⁴⁶, 4782986, F₃, 2, 20) (dual of [(4782986, 2), 9565726, 21]-NRT-code), using trace code based on linear OOA(9¹²³, 2391493, F₉, 2, 20) (dual of [(2391493, 2), 4782863, 21]-NRT-code), using

OOA 2-folding [i] based on linear OA(9¹²³, 4782986, F₉, 20) (dual of [4782986, 4782863, 21]-code), using
- constructionÂ X applied to C_e(19) âŠ‚ C_e(16) [i] based on
  1. linear OA(9¹²⁰, 4782969, F₉, 20) (dual of [4782969, 4782849, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]
  2. linear OA(9¹⁰⁶, 4782969, F₉, 17) (dual of [4782969, 4782863, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
  3. linear OA(9³, 17, F₉, 2) (dual of [17, 14, 3]-code), using
    - discarding factors / shortening the dual code based on linear OA(9³, 80, F₉, 2) (dual of [80, 77, 3]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 80Â = 9²âˆ’1, defining interval IÂ =Â [0,1], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 3 [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(3²⁴⁷, 4782986, F₃, 2, 20) (dual of [(4782986, 2), 9565725, 21]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(3²⁴⁶, 2391493, F₃, 4, 20) (dual of [(2391493, 4), 9565726, 21]-NRT-code)	[i]	OOA Folding
3	Linear OOA(3²⁴⁶, 956597, F₃, 22, 20) (dual of [(956597, 22), 21044888, 21]-NRT-code)	[i]	OOA Folding and Stacking with Additional Row