MinT - Information on Result #1540911

Information on Result #1540911

Linear OOA(4¹⁹⁵, 159381, F₄, 3, 27) (dual of [(159381, 3), 477948, 28]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(4¹⁹⁵, 159381, F₄, 27) (dual of [159381, 159186, 28]-code), using

discarding factors / shortening the dual code based on linear OA(4¹⁹⁵, 262203, F₄, 27) (dual of [262203, 262008, 28]-code), using
- 4 times code embedding in larger space [i] based on linear OA(4¹⁹¹, 262199, F₄, 27) (dual of [262199, 262008, 28]-code), using
  - constructionÂ X applied to C_e(26) âŠ‚ C_e(20) [i] based on
    1. linear OA(4¹⁸¹, 262144, F₄, 27) (dual of [262144, 261963, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
    2. linear OA(4¹³⁶, 262144, F₄, 21) (dual of [262144, 262008, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
    3. linear OA(4¹⁰, 55, F₄, 5) (dual of [55, 45, 6]-code), using
      - discarding factors / shortening the dual code based on linear OA(4¹⁰, 63, F₄, 5) (dual of [63, 53, 6]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 63Â = 4³âˆ’1, defining interval IÂ =Â [0,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]

Mode: Linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n 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(4¹⁹⁵, 31876, F₄, 33, 27) (dual of [(31876, 33), 1051713, 28]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row