MinT - Information on Result #962210

Information on Result #962210

Linear OOA(4¹⁶⁵, 87400, F₄, 3, 23) (dual of [(87400, 3), 262035, 24]-NRT-code), using OOA 3-folding based on linear OA(4¹⁶⁵, 262200, F₄, 23) (dual of [262200, 262035, 24]-code), using

1 times code embedding in larger space [i] based on linear OA(4¹⁶⁴, 262199, F₄, 23) (dual of [262199, 262035, 24]-code), using
- constructionÂ X applied to C_e(22) âŠ‚ C_e(16) [i] based on
  1. linear OA(4¹⁵⁴, 262144, F₄, 23) (dual of [262144, 261990, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
  2. linear OA(4¹⁰⁹, 262144, F₄, 17) (dual of [262144, 262035, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
  3. linear OA(4¹⁰, 55, F₄, 5) (dual of [55, 45, 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(4¹⁶⁸, 87401, F₄, 3, 23) (dual of [(87401, 3), 262035, 24]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(4¹⁶⁶, 87400, F₄, 3, 23) (dual of [(87400, 3), 262034, 24]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(4¹⁶⁷, 87400, F₄, 3, 23) (dual of [(87400, 3), 262033, 24]-NRT-code)	[i]	OOA Duplication