Lab Home | Phone | Search
	Center for Nonlinear Studies
	Home  ▶ People   Current   Affiliates   Alumni   Visitors   Students  ▶ Research   ICAM-LANL  ▶ Publications   2007   2006   2005   2004   2003   2002   2001   2000   <1999  ▶ Conferences   Workshops   Sponsorship  ▶ Talks   Colloquia   Seminars   Quantum Lunch   CMS Colloquia   Archive   Kac Lectures   Dist. Quant. Lecture   Ulam Scholar   Colloquia     Jobs  ▶ Students   Summer Research   Graduate Positions  ▶ Visitors   Description  ▶ Services   General   PD Travel Request     History of CNLS     Maps, Directions   CNLS Office   T-Division   LANL				Thursday, February 24, 201111:00 AM - 12:00 PMCNLS Conference Room (TA-3, Bldg 1690) Seminar Geometric representations of linear codes Pavel RytirCharles University, Prague We say that a linear code C is triangular representable if there exists a two dimensional simplicial complex $\Delta$ such that C is a punctured code of the kernel of the incidence matrix of $\Delta$ and there is a bijection between C and $\ker \Delta$ which maps minimal codewords to minimal codewords. We show that the linear codes over rationals and over GF(p), where p is a prime, are triangular representable. In the case of finite fields, we show that this representation determines the weight enumerator of C. We present one application of this result to the partition function of the Potts model. On the other hand, we show that there exist linear codes over any field different from rationals and GF(p), p is a prime, that are not triangular representable. We show that every construction of triangular representation fails on a very weak condition that a linear code and its triangular representation have to have the same dimension. Host: Misha Chertkov, chertkov@lanl.gov, 665-8119