MinT - Information on Result #1431437

Information on Result #1431437

Linear OOA(4²²⁵, 14702, F₄, 2, 41) (dual of [(14702, 2), 29179, 42]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(4²²⁵, 14702, F₄, 41) (dual of [14702, 14477, 42]-code), using

discarding factors / shortening the dual code based on linear OA(4²²⁵, 16433, F₄, 41) (dual of [16433, 16208, 42]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4²²⁴, 16432, F₄, 41) (dual of [16432, 16208, 42]-code), using
  - constructionÂ X applied to C_e(40) âŠ‚ C_e(33) [i] based on
    1. linear OA(4²¹¹, 16384, F₄, 41) (dual of [16384, 16173, 42]-code), using an extension C_e(40) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 4⁷âˆ’1, defining interval IÂ =Â [1,40], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 41 [i]
    2. linear OA(4¹⁷⁶, 16384, F₄, 34) (dual of [16384, 16208, 35]-code), using an extension C_e(33) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 4⁷âˆ’1, defining interval IÂ =Â [1,33], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 34 [i]
    3. linear OA(4¹³, 48, F₄, 6) (dual of [48, 35, 7]-code), using
      - discarding factors / shortening the dual code based on linear OA(4¹³, 63, F₄, 6) (dual of [63, 50, 7]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 63Â = 4³âˆ’1, defining interval IÂ =Â [0,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [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(4²²⁵, 7351, F₄, 3, 41) (dual of [(7351, 3), 21828, 42]-NRT-code)	[i]		OOA Folding