The first step is to extract the core from the cover. The amount of core you extract will be the stripped length (minus the length used to form the eye splice). You can then cut the excess cover material off, leaving about 2 fid lengths to bury.
Next, you lock stitch the core and cover just behind where the core has been extracted. Once the core and cover are locked together, you bury the empty cover into the stripped core. A good taper is important any time a dyneema line is involved. Admiral 5000 has a 24 plait cover and is very easy to taper.
Once the taper is complete, milk the core back down over the cover to complete the bury. This time of bury needs a good whipping to hold it in place. Use a good quality waxed whipping twine and whip the crossover joint to prevent the bury from pulling out. FSE Robline makes an excellent polyester whipping twine that I use for just about everything. Once the whipping is complete, we can start to form our eye splice. I've shown a locking brummel splice in these photos.
The locked brummel makes a secure eye by itself, but for optimal line strength you need a good long bury. I bury at least 4 fid lengths. The long bury will take the majority of the load on the line, and the brummel splice is just there to lock things in place. Again, since this is dyneema line we want a nice gradual taper.
Once you've milked the cover back over the tail, your splice is complete. I like to add whipping below the splice for a little extra security. This particular halyard was made for Ensign Spars and will be used on a recent total restoration of an Ensign 22.