nces 5.4.4 Correlation Properties of Derived Complex Roots-of-Unity Sequences Galois Field Connections 5.5.1 Extension Field Construction 5.5.2 The LFSR as a Galois Field Multiplier 5.5.3 Determining the Period of Memory Cell Outputs 5.5.4 The Trace Representation of M-Sequences 5.5.5 A Correlation Computation 5.5.6 Decimations of Sequences Non-Linear Feed-Forward Logic 5.6.1 A Powers-of-a Representation Theorem 5.6.2 Key's Bound on Linear Span 5.6.3 Difference Set Designs 5.6.4 GMW Sequences Direct-Sequence Multiple-Access Designs 5.7.1 A Design Criterion 5.7.2 Welch's Inner Product Bound 5.7.3 Cross-correlation of Binary M-Sequences 5.7.4 Linear Designs 5.7.5 A Transform-Domain Design Philosophy 5.7.6 Bent Sequences Frequency-Hopping Multiple-Access Designs 5.8.1 Design Criteria 5.8.2 A Bound on Hamming Distance 5.8.3 An FHMA Design Employing an M-Sequence Generator 5.8.4 Reed-Solomon Sequences A Look at the Literature 5.10 References Appendix 5A: Finite Field Arithmetic Appendix 5B: Factorizations of 2n-1 - and Selected Primitive Polynomials Contents PART 2 CLASSICAL SPREAD-SPECTRUM COMMUNICATIONS Chapter 1 Coherent Direct Sequence Systems Direct-Sequence Spread Coherent Binary Phase-Shift Keying Uncoded Bit Error Probability for Arbitrary Jammer Waveforms 1.2.1 Chernoff Bound 1.2.2 Gaussian Assumptions Uncoded Bit Error Probability for Specific Jammer Waveforms 1.3.1 CW Jammer 1.3.2 Random Jammer Pulse Jamming 1.4.1 Arbitrary Time Distribution 1.4.2 Worst Case Jammer Standard Codes and Cutoff Rates 1.5.1 The Additive White Gaussian Noise Channel 1.5.2 Jamming Channels Slow Frequency Non-Selective Fading Channels 1.6.1 Continuous Jammer with No Coding 1.6.2 Continuous Jammer with Coding-No Fading Estimate 1.6.3 Continuous Jammer with Coding-Fading Estimate 1.6.4 Pulse Jammer with No Coding Slow Fading Multipath Channels Other Coding Metrics for Pulse Jamming 1.9 Discussion 1.10 References Chapter 2 Non-Coherent Frequency-Hopped Systems Broadband Noise Jamming Worst Case Jamming 2.2.1 Partial-Band Noise Jamming