Speaker:  Prairie Wentworth-Nice, Cornell University
Title: MacWilliams Identities for Nonabelian group codes
Time: 2:30 PM, Monday, September 18, 2023
Place:  Malott 206

Abstract: In her 1961 thesis, Jesse MacWilliams published a set of formulas for linear codes that among other applications, were incredibly valuable in the study of self-dual codes. Now called the MacWilliams Identities, her results relate the code weight polynomial and complete weight enumerator of a code to those of its dual code. A similar set of MacWilliams identities has been proven to exist for many other types of codes, including abelian group codes. In 2015, Dougherty, Solé, and Kim published a list of fundamental open questions in coding theory. Among them, Open Question 4.3: "Is there a duality and MacWilliams formula for codes over non-Abelian groups?" In this talk, we propose a duality for nonabelian group codes in terms of the irreducible representations of the group. Moreover, we show that there are MacWilliams Identities which hold for this notion of duality. When the group is abelian, our results are consistent with existing formulas in the literature.


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