Bycocket is an obsolete word for a kind of cap or headdress. Its entry in the Second Edition of the Oxford English Dictionary contains this woeful note:

Through a remarkable series of blunders and ignorant reproductions of error, this word appears in modern dictionaries as ABACOT. In Hall’s Chron. a bicocket appears to have been misprinted abococket, which was copied by Grafton, altered by Holinshed to abococke, and finally ‘improved’ by Abraham Fleming to abacot (perhaps through an intermediate abacoc); hence it was again copied by Baker, inserted in his Glossarium by Spelman, and thence copied by Phillips, and so handed down through Bailey, Ash, Todd, etc., to 19th century dictionaries (some of which provide a picture of the ‘abacot’), and even inserted in dictionaries of English and foreign languages.

The OED defines abacot as a “variant of bycocket”.