MinT - Information on Result #1195412

Information on Result #1195412

Digital (53, 72, 7283)-net over F₁₆, using net defined by OOA based on linear OOA(16⁷², 7283, F₁₆, 19, 19) (dual of [(7283, 19), 138305, 20]-NRT-code), using

OOA 9-folding and stacking with additional row [i] based on linear OA(16⁷², 65548, F₁₆, 19) (dual of [65548, 65476, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(16⁷², 65551, F₁₆, 19) (dual of [65551, 65479, 20]-code), using
  - constructionÂ X applied to C_e(18) âŠ‚ C_e(14) [i] based on
    1. linear OA(16⁶⁹, 65536, F₁₆, 19) (dual of [65536, 65467, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 16⁴âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
    2. linear OA(16⁵⁷, 65536, F₁₆, 15) (dual of [65536, 65479, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 16⁴âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
    3. linear OA(16³, 15, F₁₆, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,16) or 15-cap in PG(2,16)), using
      - discarding factors / shortening the dual code based on linear OA(16³, 16, F₁₆, 3) (dual of [16, 13, 4]-code or 16-arc in PG(2,16) or 16-cap in PG(2,16)), using
        Reedâ€“Solomon code RS(13,16) [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Digital (54, 73, 7283)-net over F₁₆	[i]		Net Duplication
2	(77, 96, 7283)-net in base 8	[i]		Base Change