MinT - Information on Result #2497128

Information on Result #2497128

Linear OOA(4²⁵⁰, 524307, F₄, 2, 33) (dual of [(524307, 2), 1048364, 34]-NRT-code), using 4¹ times duplication based on linear OOA(4²⁴⁹, 524307, F₄, 2, 33) (dual of [(524307, 2), 1048365, 34]-NRT-code), using

1 times NRT-code embedding in larger space [i] based on linear OOA(4²⁴⁷, 524306, F₄, 2, 33) (dual of [(524306, 2), 1048365, 34]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4²⁴⁷, 1048612, F₄, 33) (dual of [1048612, 1048365, 34]-code), using
  - 1 times code embedding in larger space [i] based on linear OA(4²⁴⁶, 1048611, F₄, 33) (dual of [1048611, 1048365, 34]-code), using
    - constructionÂ X applied to C_e(32) âŠ‚ C_e(28) [i] based on
      1. linear OA(4²⁴¹, 1048576, F₄, 33) (dual of [1048576, 1048335, 34]-code), using an extension C_e(32) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 4¹⁰âˆ’1, defining interval IÂ =Â [1,32], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 33 [i]
      2. linear OA(4²¹¹, 1048576, F₄, 29) (dual of [1048576, 1048365, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 4¹⁰âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
      3. linear OA(4⁵, 35, F₄, 3) (dual of [35, 30, 4]-code or 35-cap in PG(4,4)), using
        discarding factors / shortening the dual code based on linear OA(4⁵, 41, F₄, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
        a cap found by Tallinii [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(4²⁵⁰, 380776, F₄, 3, 33) (dual of [(380776, 3), 1142078, 34]-NRT-code)	[i]		Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Digital (217, 250, 380776)-net over F₄	[i]		Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound