Construction of an egg coat, a specialized extracellular matrix that surrounds the ovum of animals. The egg coat provides structural support and can play an essential role in oogenesis, fertilization and early development. [ GOC:bf GOC:yaf http://www.ncbi.nlm.nih.gov/pubmed/16944418 GOC:sart http://www.ncbi.nlm.nih.gov/pubmed/17163408 ]