MinT - Information on Result #2496114

Information on Result #2496114

Linear OOA(4¹⁹², 2097165, F₄, 2, 23) (dual of [(2097165, 2), 4194138, 24]-NRT-code), using 4¹ times duplication based on linear OOA(4¹⁹¹, 2097165, F₄, 2, 23) (dual of [(2097165, 2), 4194139, 24]-NRT-code), using

1 times NRT-code embedding in larger space [i] based on linear OOA(4¹⁸⁹, 2097164, F₄, 2, 23) (dual of [(2097164, 2), 4194139, 24]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4¹⁸⁹, 4194328, F₄, 23) (dual of [4194328, 4194139, 24]-code), using
  - constructionÂ X4 applied to C_e(22) âŠ‚ C_e(20) [i] based on
    1. linear OA(4¹⁸⁸, 4194304, F₄, 23) (dual of [4194304, 4194116, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 4194303Â = 4¹¹âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
    2. linear OA(4¹⁶⁶, 4194304, F₄, 21) (dual of [4194304, 4194138, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 4194303Â = 4¹¹âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
    3. linear OA(4²³, 24, F₄, 23) (dual of [24, 1, 24]-code or 24-arc in PG(22,4)), using
      - dual of repetition code with length 24 [i]
    4. linear OA(4¹, 24, F₄, 1) (dual of [24, 23, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(4¹, s, F₄, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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		This result only	Method
1	Linear OOA(4¹⁹², 1451277, F₄, 3, 23) (dual of [(1451277, 3), 4353639, 24]-NRT-code)	[i]		Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Digital (169, 192, 1451277)-net over F₄	[i]		Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound