MinT - Information on Result #1432980

Information on Result #1432980

Linear OOA(4²³⁷, 15682, F₄, 2, 43) (dual of [(15682, 2), 31127, 44]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(4²³⁷, 15682, F₄, 43) (dual of [15682, 15445, 44]-code), using

discarding factors / shortening the dual code based on linear OA(4²³⁷, 16431, F₄, 43) (dual of [16431, 16194, 44]-code), using
- 2 times code embedding in larger space [i] based on linear OA(4²³⁵, 16429, F₄, 43) (dual of [16429, 16194, 44]-code), using
  - constructionÂ X applied to C_e(42) âŠ‚ C_e(36) [i] based on
    1. linear OA(4²²⁵, 16384, F₄, 43) (dual of [16384, 16159, 44]-code), using an extension C_e(42) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 4⁷âˆ’1, defining interval IÂ =Â [1,42], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 43 [i]
    2. linear OA(4¹⁹⁰, 16384, F₄, 37) (dual of [16384, 16194, 38]-code), using an extension C_e(36) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 4⁷âˆ’1, defining interval IÂ =Â [1,36], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 37 [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(4²³⁷, 7841, F₄, 3, 43) (dual of [(7841, 3), 23286, 44]-NRT-code)	[i]		OOA Folding