MinT - Information on Result #2495861

Information on Result #2495861

Linear OOA(4¹⁵⁹, 524307, F₄, 2, 21) (dual of [(524307, 2), 1048455, 22]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(4¹⁵⁷, 524306, F₄, 2, 21) (dual of [(524306, 2), 1048455, 22]-NRT-code), using

OOA 2-folding [i] based on linear OA(4¹⁵⁷, 1048612, F₄, 21) (dual of [1048612, 1048455, 22]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4¹⁵⁶, 1048611, F₄, 21) (dual of [1048611, 1048455, 22]-code), using
  - constructionÂ X applied to C_e(20) âŠ‚ C_e(16) [i] based on
    1. linear OA(4¹⁵¹, 1048576, F₄, 21) (dual of [1048576, 1048425, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 4¹⁰âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [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(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		Method
1	Linear OOA(4¹⁶⁰, 524307, F₄, 2, 21) (dual of [(524307, 2), 1048454, 22]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(4¹⁵⁹, 449052, F₄, 3, 21) (dual of [(449052, 3), 1346997, 22]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
3	Digital (138, 159, 449052)-net over F₄	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound