MinT - Information on Result #1429308

Information on Result #1429308

Linear OOA(4²⁰⁷, 16179, F₄, 2, 37) (dual of [(16179, 2), 32151, 38]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(4²⁰⁷, 16179, F₄, 37) (dual of [16179, 15972, 38]-code), using

discarding factors / shortening the dual code based on linear OA(4²⁰⁷, 16443, F₄, 37) (dual of [16443, 16236, 38]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4²⁰⁶, 16442, F₄, 37) (dual of [16442, 16236, 38]-code), using
  - constructionÂ X applied to C_e(36) âŠ‚ C_e(28) [i] based on
    1. 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]
    2. linear OA(4¹⁴⁸, 16384, F₄, 29) (dual of [16384, 16236, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 4⁷âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
    3. linear OA(4¹⁶, 58, F₄, 7) (dual of [58, 42, 8]-code), using
      - discarding factors / shortening the dual code based on linear OA(4¹⁶, 63, F₄, 7) (dual of [63, 47, 8]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 63Â = 4³âˆ’1, defining interval IÂ =Â [0,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [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(4²⁰⁷, 8089, F₄, 3, 37) (dual of [(8089, 3), 24060, 38]-NRT-code)	[i]		OOA Folding