MinT - Information on Result #893821

Information on Result #893821

Linear OOA(3¹⁹⁰, 4782992, F₃, 2, 15) (dual of [(4782992, 2), 9565794, 16]-NRT-code), using trace code based on linear OOA(9⁹⁵, 2391496, F₉, 2, 15) (dual of [(2391496, 2), 4782897, 16]-NRT-code), using

OOA 2-folding [i] based on linear OA(9⁹⁵, 4782992, F₉, 15) (dual of [4782992, 4782897, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(9⁹⁵, 4782993, F₉, 15) (dual of [4782993, 4782898, 16]-code), using
  - constructionÂ X applied to C_e(14) âŠ‚ C_e(11) [i] based on
    1. linear OA(9⁹², 4782969, F₉, 15) (dual of [4782969, 4782877, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
    2. linear OA(9⁷¹, 4782969, F₉, 12) (dual of [4782969, 4782898, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
    3. linear OA(9³, 24, F₉, 2) (dual of [24, 21, 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		This result only	Method
1	Linear OOA(3¹⁹¹, 4782992, F₃, 2, 15) (dual of [(4782992, 2), 9565793, 16]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(3¹⁹⁰, 2391496, F₃, 4, 15) (dual of [(2391496, 4), 9565794, 16]-NRT-code)	[i]		OOA Folding