MacWilliams was born in Stoke-on-Trent, England and studied at the University of Cambridge, receiving her BA in 1938 and her MA in the following year.
Although she did major research at Bell Labs, she was denied a promotion to a mathematics research position until she received a Ph.D. She would proceed to fulfill some of the PhD's requirements while working at Bell Labs and taking care of her family, but she completed her PhD after returning to Harvard for one more year (1961–1962), under the supervision of Andrew Gleason.
[4][5] MacWilliams worked with Gleason to produce her thesis entitled "Combinatorial Problems of Elementary Group Theory".
[7] One of MacWilliams' significant achievements was her encyclopedic book, The Theory of Error-Correcting Codes, which she wrote in collaboration with Neil Sloane[1][8] and was published in 1977.
The book is stated as being "Perhaps the most comprehensive text on the algebraic and combinatorial properties of error-correcting codes, and of abiding interest to both mathematicians and engineers.