Jessie MacWilliams

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Florence Jessie MacWilliams
Born(1917-01-04)January 4, 1917
MacWilliams identities in coding theory
Notable workThe Theory of Error-Correcting Codes, with Neil Sloane[1]
ChildrenDaughter Anne, two sons

Florence Jessie Collinson MacWilliams (4 January 1917 – 27 May 1990) was an English

MacWilliams Identity
.

Education and career

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.[3] She moved to the United States in 1939 and studied at Johns Hopkins University. One year later she left Johns Hopkins for Harvard University.

In 1955 she became a

Andrew Gleason.[4][5] MacWilliams worked with Gleason to produce her thesis entitled "Combinatorial Problems of Elementary Group Theory".[2]
Both MacWilliams and her daughter Anne, who later obtained a PhD in Mathematics, were studying mathematics at Harvard that year.

Contributions

Her formula is known as the

MacWilliams identity
, and is how MacWilliams is known. MacWilliams' result was later critical in proving an important bound on code rate, called the 'linear programming bound'.

From 1962 to 1976, Macwilliams produced important results on algebraic constructions and combinatorial properties of codes. She worked on cyclic codes, generalizing them to Abelian group codes.[6] With H.B. Mann, MacWilliams gave a solution to a difficult problem involving certain design matrices, which they published in their paper titled "On the p-rank of the design matrix of a difference set".[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. It was one of the major works responsible for laying the foundation for a revolution in communication technology that is being played out even today".[9]

Recognition

In 1980 she was the first

Noether Lecturer.[6]

References

Further reading