MinT - Information on Result #1538108

Information on Result #1538108

Linear OOA(4¹⁵⁴, 16390, F₄, 3, 27) (dual of [(16390, 3), 49016, 28]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(4¹⁵⁴, 16390, F₄, 27) (dual of [16390, 16236, 28]-code), using

discarding factors / shortening the dual code based on linear OA(4¹⁵⁴, 16432, F₄, 27) (dual of [16432, 16278, 28]-code), using
- 3 times code embedding in larger space [i] based on linear OA(4¹⁵¹, 16429, F₄, 27) (dual of [16429, 16278, 28]-code), using
  - constructionÂ X applied to C_e(26) âŠ‚ C_e(20) [i] based on
    1. linear OA(4¹⁴¹, 16384, F₄, 27) (dual of [16384, 16243, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 4⁷âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
    2. linear OA(4¹⁰⁶, 16384, F₄, 21) (dual of [16384, 16278, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 4⁷âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [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(4¹⁵⁴, 3277, F₄, 33, 27) (dual of [(3277, 33), 107987, 28]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row