Harold N. Ward

Bio: Harold N. Ward is an academic researcher from University of Virginia. The author has contributed to research in topics: Linear code & Polynomial code. The author has an hindex of 16, co-authored 57 publications receiving 1659 citations. Previous affiliations of Harold N. Ward include Brown University.

On Ree’s series of simple groups

Abstract: Ree recently discovered a series of finite simple groups related to the simple Lie algebra of type (G2) [5; 6 ] . We have determined the irreducible characters of these groups. In this work, we do not use the actual definition of Ree's groups, but only the properties (l)-(5) given below. Since these are sufficient to determine the bulk of the character tables of these groups, it is our hope that they actually characterize the groups completely. The five properties used are (1) If G is one of these groups, the order of G is even and the 2Sylow subgroup of G is elementary Abelian of order 8. (2) G has no normal subgroup of index 2. (3) There is an involution / (an element of order 2) in G such that if C(J) is the centralizer of / in G and (J ) is the group generated by / , then C(J)/(J) is isomorphic to LF(2, q), the linear fractional group in two variables over a field of q elements. Here we restrict q by q^3 (mod 8) and q^27. I t follows that C(J) is the direct product of (ƒ) and a subgroup F of G which is isomorphic to LF(2, q). In F there is an element R of order (q — l)/2f and we also have (4) If R5*l, then C(R)QC(J). Finally, there is an element S of F with order (q+l)/2. Let J' = S* where / = ( g + l ) / 4 . Then S generates the commutator subgroup of C(J, J'), the centralizer of (J , J'). We have (5) F o r S 2 , C(S*)QC(J). This condition can actually be replaced by the weaker condition (5*) Let A €N(J, J"'), the normalizer in G of (ƒ, / '>, but A $ C(J, J)Let A = 1. Then A does not commute with S. From these conditions on G we derive a number of results. The approach is almost entirely by means of characters, both ordinary and modular. Condition (4) leads to two families of exceptional characters related to the classes of R( 5^1) and JR (T^J). These characters are the characters of 2-defect 1. Results of Brauer [ l ; 2; 3] then lead to two possibilities for the principal 2-block (the 2-block containing the character which is 1 everywhere) ; one contains seven 1 This note is a summary of the results obtained in the author's Harvard University dissertation of the same title, written under the direction of Richard Brauer. 2 This research was supported by the National Science Foundation.

Ternary codes of minimum weight 6 and the classification of the self-dual codes of length 20

Abstract: Self-orthogonal ternary codes of minimum weight 3 may be analyzed in a straightforward manner using the theory of glueing introduced in earlier papers. The present paper describes a method for studying codes of minimum weight 6 : the supports of the words of weight 6 form what is called a center set. Associated with each center set is a graph, and all the graphs that can arise in this way are known. These techniques are used to classify the ternary self-dual codes of length 20 : there are 24 inequivalent codes, 17 of which are indecomposable. Six of the codes have minimum weight 6 .

Fuzzy extractors: How to generate strong keys from biometrics and other noisy data

Abstract: We provide formal definitions and efficient secure techniques for turning biometric information into keys usable for any cryptographic application, and reliably and securely authenticating biometric data.

Introduction to finite fields and their applications

Abstract: The first part of this book presents an introduction to the theory of finite fields, with emphasis on those aspects that are relevant for applications. The second part is devoted to a discussion of the most important applications of finite fields especially information theory, algebraic coding theory and cryptology (including some very recent material that has never before appeared in book form). There is also a chapter on applications within mathematics, such as finite geometries. combinatorics. and pseudorandom sequences. Worked-out examples and list of exercises found throughout the book make it useful as a textbook.

Quantum error correction via codes over GF(4)

Abstract: The unreasonable effectiveness of quantum computing is founded on coherent quantum superposition or entanglement which allows a large number of calculations to be performed simultaneously. This coherence is lost as a quantum system interacts with its environment. In the present paper the problem of finding quantum-error-correcting codes is transformed into one of finding additive codes over the field GF(4) which are self-orthogonal with respect to a certain trace inner product. Many new codes and new bounds are presented, as well as a table of upper and lower bounds on such codes of length up to 30 qubits.

Hide and seek: an introduction to steganography

Abstract: Although people have hidden secrets in plain sight-now called steganography-throughout the ages, the recent growth in computational power and technology has propelled it to the forefront of today's security techniques. Essentially, the information-hiding process in a steganographic system starts by identifying a cover medium's redundant bits (those that can be modified without destroying that medium's integrity). The embedding process creates a stego medium by replacing these redundant bits with data from the hidden message. This article discusses existing steganographic systems and presents recent research in detecting them via statistical steganalysis. Here, we present recent research and discuss the practical application of detection algorithms and the mechanisms for getting around them.

Collusion-secure fingerprinting for digital data

Abstract: This paper discusses methods for assigning code-words for the purpose of fingerprinting digital data, e.g., software, documents, music, and video. Fingerprinting consists of uniquely marking and registering each copy of the data. This marking allows a distributor to detect any unauthorized copy and trace it back to the user. This threat of detection will deter users from releasing unauthorized copies. A problem arises when users collude: for digital data, two different fingerprinted objects can be compared and the differences between them detected. Hence, a set of users can collude to detect the location of the fingerprint. They can then alter the fingerprint to mask their identities. We present a general fingerprinting solution which is secure in the context of collusion. In addition, we discuss methods for distributing fingerprinted data.