MinT - Information on Result #3266917

Information on Result #3266917

Digital (47, 70, 23832)-net over F₆₄, using 64¹ times duplication based on digital (46, 69, 23832)-net over F₆₄, using

net defined by OOA [i] based on linear OOA(64⁶⁹, 23832, F₆₄, 23, 23) (dual of [(23832, 23), 548067, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(64⁶⁹, 262153, F₆₄, 23) (dual of [262153, 262084, 24]-code), using
  - discarding factors / shortening the dual code based on linear OA(64⁶⁹, 262155, F₆₄, 23) (dual of [262155, 262086, 24]-code), using
    - constructionÂ X applied to C_e(22) âŠ‚ C_e(19) [i] based on
      1. linear OA(64⁶⁷, 262144, F₆₄, 23) (dual of [262144, 262077, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
      2. linear OA(64⁵⁸, 262144, F₆₄, 20) (dual of [262144, 262086, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]
      3. linear OA(64², 11, F₆₄, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,64)), using
        discarding factors / shortening the dual code based on linear OA(64², 64, F₆₄, 2) (dual of [64, 62, 3]-code or 64-arc in PG(1,64)), using
        Reedâ€“Solomon code RS(62,64) [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	(61, 84, 23832)-net in base 32	[i]		Base Change
2	(82, 105, 23832)-net in base 16	[i]		Base Change