Linichuk began skating due to her mother who enjoyed figure skating. She had a dozen coaches before ending up in the group of Elena Tchaikovskaia, who Linichuk soon sensed was the right coach for her.
Linichuk and Karponosov trained at Dynamo in Moscow. They won the World Universiade in 1972, and were bronze medalists at the 1974 and 1977 World Championships. They also finished 4th at the 1976 Winter Olympics, the year ice dancing was introduced as an Olympic sport.
Linichuk and Karponosov became World champions in 1978 and 1979. They won the European Championships in 1979 and 1980, after winning a silver medal in 1978, and bronze medals from 1974 through 1977.
Linichuk and Karponosov won the 1980 Olympics, but failed to defend their World title, making them the only team ever to unsuccessfully defend a World title after winning the Olympics. In 1981, Linichuk and Karponosov retired from competition.
Linichuk accepted Karponosov's proposal after they retired from competition. She had one prior marriage. Linichuk and Karponosov were married on 31 July 1981. Their daughter, Anastasiya Karponosova, was born in February 1985. The couple initially lived in Moscow and then moved to the United States in the early '90s.