Shift Register Sequences

Shift Register Sequences presents the mathematical theory and applications of linear feedback shift registers, a fundamental concept in digital sequences and coding theory. The book covers both the theoretical foundations and practical implementations of these systems. Each chapter builds systematically from basic principles of shift registers through to advanced topics like correlation properties and random number generation. The text includes detailed examples, mathematical proofs, and engineering applications relevant to communications and cryptography. The work incorporates research from the author's time at Jet Propulsion Laboratory, offering insights into real-world applications of shift register sequences in space communications and radar systems. Clear diagrams and mathematical notation support the technical content throughout. This book stands as a bridge between pure mathematics and engineering practice, demonstrating how abstract sequence theory translates into concrete technological solutions. Its influence extends across multiple fields including cryptography, spread-spectrum communications, and pseudo-random number generation.

Readers describe this book as a detailed mathematical reference on shift register sequences and their applications. Most online reviews are from researchers and engineers who use it in their work. Likes: - Clear explanations of complex mathematical concepts - Rigorous proofs and thorough technical depth - Practical applications in cryptography and communications - High quality diagrams and visual aids Dislikes: - Dense notation requires strong math background - Limited introduction/context for beginners - Out of print and difficult to obtain - High price ($200+ for used copies) From an Amazon reviewer: "Unless you already work with shift registers, this book will be nearly incomprehensible without significant study." Ratings: Amazon: 4.7/5 (11 reviews) Goodreads: 4.33/5 (6 ratings, 0 reviews) No full reviews found on other academic or engineering sites, though the book is frequently cited in research papers and technical documentation.

Theory of Linear and Integer Programming by Alexander Schrijver This text covers linear feedback shift registers and their connection to algebraic coding theory through polynomial mathematics and linear algebra.

Coding Theory: A First Course by San Ling and Chaoping Xing The book explores pseudo-random sequence generation, stream ciphers, and cyclic codes that build upon shift register principles.

Introduction to Cryptography with Coding Theory by Wade Trappe, Lawrence C. Washington This work connects shift register sequences to modern cryptographic applications and stream cipher design.

Combinatorial Mathematics by H. J. Ryser The text examines combinatorial structures and sequences with mathematical properties similar to those found in shift registers.

Digital Communications by John G. Proakis and Masoud Salehi This book connects shift register sequences to practical applications in spread spectrum communications and error-correction coding.

🔹 Solomon Golomb coined the term "polyomino" in 1953, which later inspired the game Tetris. He was the first to study these geometric shapes systematically. 🔹 The book's subject matter (shift registers) played a crucial role in early space communications, including NASA's Deep Space Network, where Golomb's work helped develop reliable communication systems. 🔹 First published in 1967, the book became so sought-after that used copies were selling for hundreds of dollars before its revised edition was released in 1981. 🔹 Shift register sequences have become fundamental to modern cryptography, digital communications, and are used in generating pseudorandom numbers for computer simulations. 🔹 Author Solomon Golomb was awarded the National Medal of Science by President Obama in 2013, recognizing his pioneering work in shift register sequences and communications technology.