MinT - Information on Result #1436065

Information on Result #1436065

Linear OOA(4²⁵⁹, 61254, F₄, 2, 40) (dual of [(61254, 2), 122249, 41]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(4²⁵⁹, 61254, F₄, 40) (dual of [61254, 60995, 41]-code), using

discarding factors / shortening the dual code based on linear OA(4²⁵⁹, 65603, F₄, 40) (dual of [65603, 65344, 41]-code), using
- 5 times code embedding in larger space [i] based on linear OA(4²⁵⁴, 65598, F₄, 40) (dual of [65598, 65344, 41]-code), using
  - constructionÂ X applied to C([0,20]) âŠ‚ C([0,16]) [i] based on
    1. linear OA(4²⁴¹, 65537, F₄, 41) (dual of [65537, 65296, 42]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 4¹⁶âˆ’1, defining interval IÂ =Â [0,20], and minimum distance dÂ â‰¥ |{−20,−19,…,20}|+1Â =Â 42 (BCH-bound) [i]
    2. linear OA(4¹⁹³, 65537, F₄, 33) (dual of [65537, 65344, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 4¹⁶âˆ’1, defining interval IÂ =Â [0,16], and minimum distance dÂ â‰¥ |{−16,−15,…,16}|+1Â =Â 34 (BCH-bound) [i]
    3. linear OA(4¹³, 61, F₄, 6) (dual of [61, 48, 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(4²⁵⁹, 30627, F₄, 3, 40) (dual of [(30627, 3), 91622, 41]-NRT-code)	[i]		OOA Folding