MinT - Information on Result #1431194

Information on Result #1431194

Linear OOA(4²²³, 13691, F₄, 2, 41) (dual of [(13691, 2), 27159, 42]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(4²²³, 13691, F₄, 41) (dual of [13691, 13468, 42]-code), using

discarding factors / shortening the dual code based on linear OA(4²²³, 16425, F₄, 41) (dual of [16425, 16202, 42]-code), using
- 2 times code embedding in larger space [i] based on linear OA(4²²¹, 16423, F₄, 41) (dual of [16423, 16202, 42]-code), using
  - constructionÂ X applied to C([0,20]) âŠ‚ C([0,17]) [i] based on
    1. linear OA(4²¹¹, 16385, F₄, 41) (dual of [16385, 16174, 42]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385Â | 4¹⁴âˆ’1, defining interval IÂ =Â [0,20], and minimum distance dÂ â‰¥ |{−20,−19,…,20}|+1Â =Â 42 (BCH-bound) [i]
    2. linear OA(4¹⁸³, 16385, F₄, 35) (dual of [16385, 16202, 36]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385Â | 4¹⁴âˆ’1, defining interval IÂ =Â [0,17], and minimum distance dÂ â‰¥ |{−17,−16,…,17}|+1Â =Â 36 (BCH-bound) [i]
    3. linear OA(4¹⁰, 38, F₄, 5) (dual of [38, 28, 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(4²²³, 6845, F₄, 3, 41) (dual of [(6845, 3), 20312, 42]-NRT-code)	[i]		OOA Folding