MinT - Information on Result #1539405

Information on Result #1539405

Linear OOA(4¹⁷⁴, 131096, F₄, 3, 25) (dual of [(131096, 3), 393114, 26]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(4¹⁷⁴, 131096, F₄, 2, 25) (dual of [(131096, 2), 262018, 26]-NRT-code), using

OOA 2-folding [i] based on linear OA(4¹⁷⁴, 262192, F₄, 25) (dual of [262192, 262018, 26]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4¹⁷³, 262191, F₄, 25) (dual of [262191, 262018, 26]-code), using
  - constructionÂ X applied to C([0,12]) âŠ‚ C([0,9]) [i] based on
    1. linear OA(4¹⁶³, 262145, F₄, 25) (dual of [262145, 261982, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145Â | 4¹⁸âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]
    2. linear OA(4¹²⁷, 262145, F₄, 19) (dual of [262145, 262018, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145Â | 4¹⁸âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]
    3. linear OA(4¹⁰, 46, F₄, 5) (dual of [46, 36, 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(4¹⁷⁵, 131096, F₄, 3, 25) (dual of [(131096, 3), 393113, 26]-NRT-code)	[i]		OOA Duplication