MinT - Information on Result #1426437

Information on Result #1426437

Linear OOA(4¹⁸⁰, 15678, F₄, 2, 32) (dual of [(15678, 2), 31176, 33]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(4¹⁸⁰, 15678, F₄, 32) (dual of [15678, 15498, 33]-code), using

discarding factors / shortening the dual code based on linear OA(4¹⁸⁰, 16430, F₄, 32) (dual of [16430, 16250, 33]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4¹⁷⁹, 16429, F₄, 32) (dual of [16429, 16250, 33]-code), using
  - constructionÂ X applied to C_e(32) âŠ‚ C_e(25) [i] based on
    1. linear OA(4¹⁶⁹, 16384, F₄, 33) (dual of [16384, 16215, 34]-code), using an extension C_e(32) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 4⁷âˆ’1, defining interval IÂ =Â [1,32], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 33 [i]
    2. linear OA(4¹³⁴, 16384, F₄, 26) (dual of [16384, 16250, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 4⁷âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [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(4¹⁸⁰, 7839, F₄, 3, 32) (dual of [(7839, 3), 23337, 33]-NRT-code)	[i]		OOA Folding