MinT - Information on Result #2496944

Information on Result #2496944

Linear OOA(4²⁴⁵, 524320, F₄, 2, 31) (dual of [(524320, 2), 1048395, 32]-NRT-code), using 2 times NRT-code embedding in larger space based on linear OOA(4²⁴¹, 524318, F₄, 2, 31) (dual of [(524318, 2), 1048395, 32]-NRT-code), using

OOA 2-folding [i] based on linear OA(4²⁴¹, 1048636, F₄, 31) (dual of [1048636, 1048395, 32]-code), using
- constructionÂ X applied to C_e(30) âŠ‚ C_e(24) [i] based on
  1. linear OA(4²³¹, 1048576, F₄, 31) (dual of [1048576, 1048345, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 4¹⁰âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
  2. linear OA(4¹⁸¹, 1048576, F₄, 25) (dual of [1048576, 1048395, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 4¹⁰âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [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(4²⁴⁶, 524320, F₄, 2, 31) (dual of [(524320, 2), 1048394, 32]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(4²⁴⁵, 524320, F₄, 3, 31) (dual of [(524320, 3), 1572715, 32]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
3	Digital (214, 245, 524320)-net over F₄	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound