MinT - Information on Result #1431073

Information on Result #1431073

Linear OOA(4²²², 15860, F₄, 2, 40) (dual of [(15860, 2), 31498, 41]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(4²²², 15860, F₄, 40) (dual of [15860, 15638, 41]-code), using

discarding factors / shortening the dual code based on linear OA(4²²², 16430, F₄, 40) (dual of [16430, 16208, 41]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4²²¹, 16429, F₄, 40) (dual of [16429, 16208, 41]-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(4¹⁰, 45, F₄, 5) (dual of [45, 35, 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(4²²², 7930, F₄, 3, 40) (dual of [(7930, 3), 23568, 41]-NRT-code)	[i]		OOA Folding