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Creators/Authors contains: "Colbourn, Charles"

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  1. (, International journal of group theory)
    By exploiting symmetries of finite fields, covering perfect hash families provide a succinct representation for covering arrays of index one. For certain parameters, this connection has led to both the best current asymptotic existence results and the best known efficient construction algorithms for covering arrays. The connection generalizes in a straightforward manner to arrays in which every t-way interaction is covered λ > 1 times, i.e., to covering arrays of index more than one. Using this framework, we focus on easily computed, explicit upper bounds on numbers of rows for various parameters with higher index. 
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    Free, publicly-accessible full text available December 31, 2025
  2. ; (, Information and Computation)
    Detecting arrays provide test suites for complex engineered systems in which many factors interact. The determination of which interactions have a significant impact on system behaviour requires not only that each interaction appear in a test, but also that its effect can be distinguished from those of other significant interactions. In this paper, compact representations of detecting arrays using vectors over the finite field are developed. Covering strong separating hash families exploit linear independence over the field, while the weaker elongated covering perfect hash families permit some linear dependence. For both, probabilistic analyses are employed to establish effective upper bounds on the number of tests needed in a detecting array for a wide variety of parameters. The analyses underlie efficient algorithms for the explicit construction of detecting arrays. 
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    Free, publicly-accessible full text available December 1, 2025
  3. ; ; (, Springer)
    Hoffman, Frederick; Holliday, Sarah; Rosen, Zvi; Shahrokhi, Farhad; Wierman, John (Ed.)
    For a finite field of order.q, and.v a divisor of.q − 1, additive translates of a cyclotomic vector yield a.q × q cyclotomic array on.v symbols. For every positive integer.t, for certain.q sufficiently large with respect to.v, such a cyclotomic array is always a covering array of strength.t. Asymptotically such arrays have far too many rows to be competitive with certain other covering array constructions. Nevertheless, for small values of .t , this cyclotomic method produces smallest known covering arrays for numerous parameters suitable for practical application. This paper extends these ideas and shows that cyclotomy can produce covering arrays of higher index, and locating and detecting arrays with large separation. Computational results also demonstrate that certain cyclotomic arrays for the same order.q but different values of .v can be juxtaposed to produce mixed-level covering, locating, and detecting arrays. 
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    Accepted Manuscript Full Text Available
  4. ; ; ; ; (, Journal of Quality Technology)
    Alternative design and analysis methods for screening experiments based on locating arrays are presented. The number of runs in a locating array grows logarithmically based on the number of factors, providing efficient methods for screening complex engineered systems, especially those with large numbers of categorical factors having different numbers of levels. Our analysis method focuses on levels of factors in the identification of important main effects and two-way interactions. We demonstrate the validity of our design and analysis methods on both well-studied and synthetic data sets and investigate both statistical and combinatorial properties of locating arrays that appear to be related to their screening capability. 
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    Full Text Available 
  5. (, Discrete Mathematics)
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  6. ; ; (, Applied mathematics and computation)
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  7. ; ; ; ; (, 2022 IEEE International Symposium on Information Theory (ISIT))
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  8. (, Designs, Codes and Cryptography)
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  9. (, Graphs and Combinatorics)
    null (Ed.)
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  10. (, 2020 Algebraic and Combinatorial Coding Theory (ACCT))
    null (Ed.)
    Full Text Available