MinT - Information on Result #1543714

Information on Result #1543714

Linear OOA(4²²⁸, 131096, F₄, 3, 33) (dual of [(131096, 3), 393060, 34]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(4²²⁸, 131096, F₄, 2, 33) (dual of [(131096, 2), 261964, 34]-NRT-code), using

OOA 2-folding [i] based on linear OA(4²²⁸, 262192, F₄, 33) (dual of [262192, 261964, 34]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4²²⁷, 262191, F₄, 33) (dual of [262191, 261964, 34]-code), using
  - constructionÂ X applied to C([0,16]) âŠ‚ C([0,13]) [i] based on
    1. linear OA(4²¹⁷, 262145, F₄, 33) (dual of [262145, 261928, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145Â | 4¹⁸âˆ’1, defining interval IÂ =Â [0,16], and minimum distance dÂ â‰¥ |{−16,−15,…,16}|+1Â =Â 34 (BCH-bound) [i]
    2. linear OA(4¹⁸¹, 262145, F₄, 27) (dual of [262145, 261964, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145Â | 4¹⁸âˆ’1, defining interval IÂ =Â [0,13], and minimum distance dÂ â‰¥ |{−13,−12,…,13}|+1Â =Â 28 (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(4²²⁹, 131096, F₄, 3, 33) (dual of [(131096, 3), 393059, 34]-NRT-code)	[i]		OOA Duplication