MinT - Information on Result #1431199

Information on Result #1431199

Linear OOA(4²²³, 49229, F₄, 2, 35) (dual of [(49229, 2), 98235, 36]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(4²²³, 49229, F₄, 35) (dual of [49229, 49006, 36]-code), using

discarding factors / shortening the dual code based on linear OA(4²²³, 65590, F₄, 35) (dual of [65590, 65367, 36]-code), using
- 4 times code embedding in larger space [i] based on linear OA(4²¹⁹, 65586, F₄, 35) (dual of [65586, 65367, 36]-code), using
  - constructionÂ X applied to C_e(34) âŠ‚ C_e(28) [i] based on
    1. linear OA(4²⁰⁹, 65536, F₄, 35) (dual of [65536, 65327, 36]-code), using an extension C_e(34) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 4⁸âˆ’1, defining interval IÂ =Â [1,34], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 35 [i]
    2. linear OA(4¹⁶⁹, 65536, F₄, 29) (dual of [65536, 65367, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 4⁸âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
    3. linear OA(4¹⁰, 50, F₄, 5) (dual of [50, 40, 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, 24614, F₄, 3, 35) (dual of [(24614, 3), 73619, 36]-NRT-code)	[i]		OOA Folding