How does pseudo-random noise increase DCF77 accuracy
According to Meinberg:

The carrier frequency of 77.5 kHz is amplitude-modulated (AM) with time marks at the beginning of each second. Radio clocks decode those time marks in order to yield the current date, time, and status. Since the AM signal is often superimposed by interfering noise, there received signal must be filtered with low bandwidth, causing a skew and a jitter of the demodulated time code in the range of 10±3 ms.
This accuracy is often not suitable for modern applications, so the PTB introduced an additional modulation which allows for increased accuracy using correlation techniques for the receiver.
In addition to the AM, the carrier signal is phase-modulated with a pseudo-random noise sequence (PZF, PRN). The PRN sequence contains 512 bits which are transmitted by phase modulation between the AM time marks, including the same number of logical '0' and logical '1' bits to keep the average phase of the carrier signal unchanged. The maximum phase deviation is ±10° and the length of one bit corresponds to 120 periods of the 77.5 kHz carrier frequency, i.e. 1.55 ms. The complete PRN sequence is transmitted once every second, starting 200 ms after the beginning of a new second and ending shortly before the next one.
The phase modulated signal can be received with higher bandwith than the AM signal. The radio clock generates the same PRN sequence locally and uses correlation techniques to derive the time frames with a dispersion of a few microseconds only. Additionally, correlation technique provides a high degree of immunity against interference and electrical noise.

(my emphasis)
More details of the PRN algorithm etc are at the usual place
Even more details in PTB paper 1988