Martin Cohn

A class of balanced binary sequences with optimal autocorrelation properties

The construction of a class of balanced binary sequences with optimal autocorrelation properties is described. Given any odd prime p and any positive integer m , a balanced ( \pm 1) binary sequence of length p^{m} - 1 whose cyclic autocorrelation function c (\tau) satisfies c (0) = p^{m} - 1 , and, for \tau \neq 0, c (\tau) = +2 or -2 when (p^{m} - 1)/2 is odd, and c(\tau) = 0 or -4 when (p^{m} - 1)/2 is even is constructed. Optimality is proved by showing that every balanced binary sequence has at least two distinct out-of-phase correlation values which are at least as large as those obtained here.

On fast M-sequence transforms (Corresp.)

The equivalence of M -sequence matrices to Walsh-Hadamard matrices can be exploited to take advantage of the latters fast transform algorithm. The nature of the obvious equivalence, its relation to the M -sequence and its implementation as address modifications realized by linear feedback shift-registers are discussed.

Maximal families of bent sequences

In a recent paper Olsen, Scholtz, and Welch (OSW) describe the use of bent functions to construct families of sequences with asymptotically optimal correlation properties. We show that the sequences produced by the OSW construction possess the claimed correlation properties if and only if the underlying bent functions are pairwise orthogonal. Consequently, the cardinality of a family of OSW sequences of length 2^{n}-1 cannot exceed 2^{n/2} . We also describe methods of selecting a maximal set of orthogonal bent functions.

Cycle decomposition by disjoint transpositions

Abstract We investigate in this paper the cycle structures induced on cyclic permutations by disjoint transpositions or, equivalently, the decomposition of a statecycle by interchanging the successors of disjoint state pairs. In both cases we relate the number of resulting cycles to a binary matrix which in a simple manner describes the interaction of the modifications. A possible application to an outstanding problem in shift-register cycle structures is described.

Design of universal test sequences for VLSI

A test sequence is called (s,t) -universal if it exercises every function depending on t or fewer inputs on a very large scale integration (VLSI) chip with s inputs. Randomized and deterministic procedures are deseribed for the design of (s,t) -universal sequences and for the signature analysis of the test outputs.

Identification and Minimization of Linear Machines

This paper is a study of linear machines and their submachines. Methods are presented for finding the reduced form of a given linear machine with or without fixed initial state. A technique is suggested for detecting whether a machine is linear or can be embedded as a submachine in a linear machine. In the latter case a state assignment is produced for the minimum linear realization. Encoded inputs and outputs are assumed, but given machines are not assumed reduced, nor are there any restrictions on the number of states in the given machine or in the linear realization. The method also detects machines that are linearly realizable when constants are available. The main results are that the reduced form of a linear machine is linear and that a linearly realizable machine with r-independent states has an r-dimensional realization.

Affine m-ary gray codes

This paper presents a nontable-lookup technique for generating a class of n-dimensional m-ary Gray codes for every pair (n, m) of integers. It does not seek to exhaust all such codes, but restricts itself to a class characterized by simple encoding and decoding schemes. The simplicity shows up not only in the mathematical description of these codes as affine transforms of the sequence of m-ary numbers, but also in the circuitry required for realizations. For instance, a serial decoder can be built of a single unit delay and a single modular adder.

An algorithm for optimal prefix parsing of a noiseless and memoryless channel

We discuss the prefix encoding of a Q -ary source (Q \geq 2) into an L -symbol channel alphabet with L \geq Q . We present an optimal encoding scheme that minimizes the expected cost per symbol in the case of equally probable source symbols and arbitrary channel symbol costs.

A Gray Code Counter

A Gray code counter which has an iterative and relatively simple structure is described. The code is shown to be the reflected binary Gray code, implying simple conversion of the count into binary code.

Design of Adaptive Procedures for Fault Detection and Isolation

An algorithm is presented for designing minimum-expected-cost test trees for detecting and isolating single faults in a system. A test is specified by the subset of components that must be good for the test to pass, and with each test is associated a fixed cost. Each component is assumed to have an a priori probability of failure. The test tree specifies an adaptive testing procedure that detects a failure and isolates the faulty component while minimizing the expected cost of testing.