김종락

Archive of posts with tag '김종락'

  • Jon-Lark Kim (김종락), Introduction to Boolean functions with Artificial Neural Network

    IBS/KAIST Joint Discrete Math Seminar

    Introduction to Boolean functions with Artificial Neural Network
    Jon-Lark Kim (김종락)
    Department of Mathematics, Sogang University, Seoul
    2019/04/18 Thu 11:00AM-12:00PM (IBS, Room B232)
    A Boolean function is a function from the set Q of binary vectors of length n (i.e., the binary n-dimensional hypercube) to F2={0,1}. It has several applications to complexity theory, digital circuits, coding theory, and cryptography.In this talk we give a connection between Boolean functions and Artificial Neural Network. We describe how to represent Boolean functions by Artificial Neural Network including linear and polynomial threshold units and sigmoid units. For example, even though a linear threshold function cannot realize XOR, a polynomial threshold function can do it. We also give currently open problems related to the number of (Boolean) linear threshold functions and polynomial threshold functions.
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  • Jon-Lark Kim (김종락), A New Class of Linear Codes for Cryptographic Uses
    A New Class of Linear Codes for Cryptographic Uses
    Jon-Lark Kim (김종락)
    Department of Mathematics, University of Louisville, Louisville, KY, USA
    2011/11/25 Fri 2PM-3PM

    We introduce a new class of rate one half codes, called complementary information set codes. A binary linear code of length 2n and dimension n is called a complementary information set code (CIS code for short) if it has two disjoint information sets. This class of codes contains self-dual codes as a subclass. It is connected to graph correlation immune functions of use in the security of hardware implementations of  cryptographic primitives. In this talk, we give optimal or best known CIS codes of length <132. We  derive general constructions based on cyclic codes, double circulant codes, strongly regular graphs, and doubly regular tournaments. We derive a Varshamov-Gilbert bound for long CIS codes, and show that they can all be classified in small lengths up to 12 by the building up construction. This is a joint work with Claude Carlet, Philippe Gaborit, and Patrick Sole.

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  • Jon-Lark Kim (김종락), On self-dual codes
    On self-dual codes
    Jon-Lark Kim (김종락)
    Department of Mathematics, University of Louisville, Louisville, KY, USA
    2010/7/29 Thu 4PM-5PM

    Self-dual codes have become one of the most active research areas in coding theory due to their rich mathematical theories. In this talk, we start with an introduction to coding theory. Then we describe some recent results on the constructions of self-dual codes over rings, and applications to lattices and network coding theory. We conclude the talk with some open problems.

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