MinT - Information on Result #2496529

Information on Result #2496529

Linear OOA(4²¹³, 524319, F₄, 2, 27) (dual of [(524319, 2), 1048425, 28]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(4²¹¹, 524318, F₄, 2, 27) (dual of [(524318, 2), 1048425, 28]-NRT-code), using

OOA 2-folding [i] based on linear OA(4²¹¹, 1048636, F₄, 27) (dual of [1048636, 1048425, 28]-code), using
- constructionÂ X applied to C_e(26) âŠ‚ C_e(20) [i] based on
  1. linear OA(4²⁰¹, 1048576, F₄, 27) (dual of [1048576, 1048375, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 4¹⁰âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
  2. linear OA(4¹⁵¹, 1048576, F₄, 21) (dual of [1048576, 1048425, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 4¹⁰âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
  3. linear OA(4¹⁰, 60, F₄, 5) (dual of [60, 50, 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: Constructive and 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		Method
1	Linear OOA(4²¹⁴, 524319, F₄, 2, 27) (dual of [(524319, 2), 1048424, 28]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(4²¹³, 524319, F₄, 3, 27) (dual of [(524319, 3), 1572744, 28]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
3	Digital (186, 213, 524319)-net over F₄	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound