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The 4th International Conference on Ad-Hoc Networks and Wireless (ADHOC- NOW 2005)was held October 6-8,2005in Cancun, Mexico. Adhoc Now started as a workshop in 2002 and was held at the Fields Institute in Toronto. In 2003, it was held in Montreal, and in 2004 it was held in Vancouver. 2005 was the ?rst yearfortheconferencetomoveoutsideofCanada.Thepurposeoftheconference is to create a collaborative forum between mathematicians, computer scientists, and engineers for research in the ?eld of mobile ad hoc and sensor networks. In 2005, we received over 100 submissions from 22 di?erent countries: Australia,Canada,China,France,Germany,Greece,India,Ireland,Italy,Japan, Korea, Malaysia, Mexico, Nepal, Nigeria, Pakistan, Poland, Spain, Sweden, Tunisia, the UK, and the USA a true international conference. Of the papers submitted, we selected 27 for presentation at the conference and publication in the proceedings. We are grateful to our Technical Program, Organizing, and Steering C- mittees; without their help, expertise, and experiencewe could not haveselected such a ?ne program. We thank Jorge Urrutia of the Instituto de Matem´ aticas, Universidad NacionalAut´ onoma de M´ exico,and J.J. Garcia-Luna-Acevesof the Computer Engineering Department, University of California, Santa Cruz for - cepting our invitation to speak at the conference. Special thanks are due to the crewfromtheFacultaddeCienciasF´ ?sico-Matem´ aticasUniversidadMichoacana for handling the local arrangements, and to the Mobile Adhoc Research Lab at Arizona State University for handling odd jobs on a moment's notice.

Computer communication systems. --- Software engineering. --- Information storage and retrieval. --- Application software. --- Computers and civilization. --- Electrical engineering. --- Computer Communication Networks. --- Software Engineering. --- Information Storage and Retrieval. --- Information Systems Applications (incl. Internet). --- Computers and Society. --- Communications Engineering, Networks.

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Computer communication systems. --- Software engineering. --- Information storage and retrieval. --- Application software. --- Computers and civilization. --- Electrical engineering. --- Computer Communication Networks. --- Software Engineering. --- Information Storage and Retrieval. --- Information Systems Applications (incl. Internet). --- Computers and Society. --- Communications Engineering, Networks. --- Mobile communication systems --- Wireless communication systems --- Ad hoc networks (Computer networks)

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Computer communication systems. --- Software engineering. --- Information storage and retrieval. --- Application software. --- Computers and civilization. --- Electrical engineering. --- Computer Communication Networks. --- Software Engineering. --- Information Storage and Retrieval. --- Information Systems Applications (incl. Internet). --- Computers and Society. --- Communications Engineering, Networks. --- Mobile communication systems --- Wireless communication systems --- Ad hoc networks (Computer networks)

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The volume covers wide-ranging topics from Theory: structure of finite fields, normal bases, polynomials, function fields, APN functions. Computation: algorithms and complexity, polynomial factorization, decomposition and irreducibility testing, sequences and functions. Applications: algebraic coding theory, cryptography, algebraic geometry over finite fields, finite incidence geometry, designs, combinatorics, quantum information science.

Finite fields (Algebra) --- Modular fields (Algebra) --- Algebra, Abstract --- Algebraic fields --- Galois theory --- Modules (Algebra)