MinT - Information on Result #962219

Information on Result #962219

Linear OOA(4¹⁸³, 349546, F₄, 3, 23) (dual of [(349546, 3), 1048455, 24]-NRT-code), using OOA 3-folding based on linear OA(4¹⁸³, 1048638, F₄, 23) (dual of [1048638, 1048455, 24]-code), using

2 times code embedding in larger space [i] based on linear OA(4¹⁸¹, 1048636, F₄, 23) (dual of [1048636, 1048455, 24]-code), using
- constructionÂ X applied to C_e(22) âŠ‚ C_e(16) [i] based on
  1. linear OA(4¹⁷¹, 1048576, F₄, 23) (dual of [1048576, 1048405, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 4¹⁰âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
  2. linear OA(4¹²¹, 1048576, F₄, 17) (dual of [1048576, 1048455, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 4¹⁰âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [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(4¹⁸⁶, 349547, F₄, 3, 23) (dual of [(349547, 3), 1048455, 24]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(4¹⁸⁴, 349546, F₄, 3, 23) (dual of [(349546, 3), 1048454, 24]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(4¹⁸⁵, 349546, F₄, 3, 23) (dual of [(349546, 3), 1048453, 24]-NRT-code)	[i]	OOA Duplication