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Golomb and Lloyd R. WelchSolomon W. Golomb and Lloyd R. Welchhttps://doi.org/10.1137/0118025PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] S. W. Golomb and , E. C. Posner, Rook domains, Latin squares, affine planes, and error-distributing codes, IEEE Trans. Information Theory, IT-10 (1964), 196–208 10.1109/TIT.1964.1053680 MR0168394 (29:5657) 0124.11404 CrossrefISIGoogle Scholar[2] S. W. Golomb and , E. C. Posner, Hypercubes of nonnegative integers, Bull. Amer. Math. Soc., 71 (1965), 587– CrossrefISIGoogle Scholar[3] H. S. M. Coxeter, Regular polytopes, Second edition, The Macmillan Co., New York, 1963xx+321 pp. (8 plates) MR0151873 (27:1856) 0118.35902 Google Scholar[4] S. Chaude Shannon, A mathematical theory of communication, Bell System Tech. J., 27 (1948), 379–423, 623–656 MR0026286 (10,133e) CrossrefGoogle Scholar[5] Hermann Minkowski, Quelques nouveaux nouveaux thèoremes sur l'approximation des quantites a l'aide de nombres rationnels, Bulletin des sciences mathématique (2), 25 (), 72–76 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails 1-Perfect Codes Over the Quad-CubeIEEE Transactions on Information Theory, Vol. 68, No. 10 Cross Ref Partitions into Perfect Codes in the Hamming and Lee Metrics4 October 2022 | Problems of Information Transmission, Vol. 58, No. 3 Cross Ref Lattice packings of cross‐polytopes from Reed–Solomon codes and Sidon sets29 June 2022 | Bulletin of the London Mathematical Society, Vol. 18 Cross Ref Perfect t-codes in Cayley graphs of groups19 April 2021 | Discrete Mathematics, Algorithms and Applications, Vol. 14, No. 02 Cross Ref Topological Quantum Codes11 May 2022 Cross Ref Perfect codes in Euclidean lattices12 February 2021 | Computational and Applied Mathematics, Vol. 40, No. 2 Cross Ref Obtaining Binary Perfect Codes Out of TilingsIEEE Transactions on Information Theory, Vol. 66, No. 10 Cross Ref No lattice tiling of Zn by Lee sphere of radius 2Journal of Combinatorial Theory, Series A, Vol. 171 Cross Ref On the non-existence of linear perfect Lee codes: The Zhang–Ge condition and a new polynomial criterionEuropean Journal of Combinatorics, Vol. 83 Cross Ref Steganographic schemes from perfect codes on Cayley graphs2 March 2019 | Designs, Codes and Cryptography, Vol. 87, No. 10 Cross Ref Runlength-Limited Sequences and Shift-Correcting Codes: Asymptotic AnalysisIEEE Transactions on Information Theory, Vol. 65, No. 8 Cross Ref On the nonexistence of lattice tilings of Zn by Lee spheresJournal of Combinatorial Theory, Series A, Vol. 165 Cross Ref Bounds on Codes for the Bit-Shift Channel with (d,k)-Constrained Inputs Cross Ref Metrics which turn tilings into binary perfect codes Cross Ref Perfect Codes in Euclidean Lattices: Bounds and Case Studies Cross Ref Fault-Tolerant Dot-Product EnginesIEEE Transactions on Information Theory, Vol. 65, No. 4 Cross Ref Codes in the Space of Multisets—Coding for Permutation Channels With ImpairmentsIEEE Transactions on Information Theory, Vol. 64, No. 7 Cross Ref Quasi-perfect codes in the $$\\ell _p$$ ℓ p metric8 August 2016 | Computational and Applied Mathematics, Vol. 37, No. 2 Cross Ref Restriction conditions on PL(7, 2) codes (3 ≤ |𝓖 i | ≤ 7)2 April 2018 | Open Mathematics, Vol. 16, No. 1 Cross Ref 50 Years of the Golomb–Welch ConjectureIEEE Transactions on Information Theory, Vol. 64, No. 4 Cross Ref 2-Correcting Lee Codes: (Quasi)-Perfect Spectral Conditions and Some ConstructionsIEEE Transactions on Information Theory, Vol. 64, No. 4 Cross Ref Non-Existence of Linear Perfect Lee Codes With Radius 2 for Infinitely Many DimensionsIEEE Transactions on Information Theory, Vol. 64, No. 4 Cross Ref Lattice Codes for Deletion and Repetition ChannelsIEEE Transactions on Information Theory, Vol. 64, No. 3 Cross Ref Orthogonal Polynomials in Information Theory2 July 2017 Cross Ref Perfect and Quasi-Perfect Codes Under the $l_{p}$ MetricIEEE Transactions on Information Theory, Vol. 63, No. 7 Cross Ref Nonexistence of perfect 2 -error-correcting Lee codes in certain dimensionsEuropean Journal of Combinatorics, Vol. 63 Cross Ref Improved Bounds on Sidon Sets via Lattice Packings of SimplicesMladen Kovačević and Vincent Y. 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Optimization and the Geometry of Numbers: Packing and CoveringThomas L. Saaty and Joyce M. Alexander18 July 2006 | SIAM Review, Vol. 17, No. 3AbstractPDF (3800 KB)Splittings of cyclic groups, tilings of Euclidean space, and perfect shift codes Cross Ref On the optimality of coloring with a lattice Cross Ref Optimal interleaving schemes for correcting 2-D cluster errors Cross Ref Optimal t-interleaving on tori Cross Ref User traffic multiplexing on OFDM downlink Cross Ref Frequency coded waveforms for enhanced delay-Doppler resolution Cross Ref Volume 18, Issue 2| 1970SIAM Journal on Applied Mathematics History Submitted:27 January 1968Published online:01 August 2006 InformationCopyright © 1970 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0118025Article page range:pp. 302-317ISSN (print):0036-1399ISSN (online):1095-712XPublisher:Society for Industrial and Applied Mathematics","publishedDate","1970-03-01","publishedYear",1970,"venue","SIAM Journal on Applied Mathematics",233,"authors","keywords",[156,157,158],"pdfUrl","topVenue","graph theory and CDMA systems","Coding theory and cryptography","DNA and Biological Computing","paper_W2011059145","Bent-function sequences","{\"openalex\":\"W2011059145\",\"doi\":\"10.1109/tit.1982.1056589\"}","2026-05-22T02:19:07.429140224","2026-05-22T02:19:07.429141958","10.1109/tit.1982.1056589","W2011059145","In this paper we construct a new family of nonlinear binary signal sets which achieve Welch's lower bound on simultaneous cross correlation and autocorrelation magnitudes. Given a parameter n with n=0 \\pmod{4} , the period of the sequences is 2^{n}-1 , the number of sequences in the set is 2^{n/2} , and the cross/auto correlation function has three values with magnitudes \\leq 2^{n/2}+1 . The equivalent linear span of the codes is bound above by \\sum_{i=1}^{n/4}\\left(\\stackrel{n}{i} \\right) . These new signal sets have the same size and correlation properties as the small set of Kasami codes, but they have important advantages for use in spread spectrum multiple access communications systems. First, the sequences are \"balances,\" which represents only a slight advantage. Second, the sequence generators are easy to randomly initialize into any assigned code and hence can be rapidly \"hopped\" from sequence to sequence for code division multiple access operation. Most importantly, the codes are nonlinear in that the order of the linear difference equation satisfied by the sequence can be orders of magnitude larger than the number of memory elements in the generator that produced it. This high equivalent linear span assures that the code sequence cannot be readily analyzed by a sophisticated enemy and then used to neutralize the advantages of the spread spectrum processing.","1982-11-01",1982,"IEEE Transactions on Information Theory",268,[157,156,172],"Cellular Automata and Applications","paper_W2032685643","Generalized bent functions and their properties","{\"openalex\":\"W2032685643\",\"doi\":\"10.1016/0097-3165(85)90049-4\"}","2026-05-16T13:41:53.460075464","2026-05-19T06:35:52.332094241","10.1016/0097-3165(85)90049-4","W2032685643","1985-09-01",1985,"Journal of Combinatorial Theory Series A",449,[157,156,185],"Cancer Mechanisms and Therapy","paper_W2109084006","New upper bounds on the rate of a code via the Delsarte-MacWilliams inequalities","{\"openalex\":\"W2109084006\",\"doi\":\"10.1109/tit.1977.1055688\"}","2026-05-16T12:26:33.220399293","2026-05-19T05:58:31.196213563","10.1109/tit.1977.1055688","W2109084006","With the Delsarte-MacWilliams inequalities as a starting point, an upper bound is obtained on the rate of a binary code as a function of its minimum distance. This upper bound is asymptotically less than Levenshtein's bound, and so also Elias's.","1977-03-01",1977,455,[157,156,198],"Finite Group Theory Research","paper_W2138548210","Lower bounds on the maximum cross correlation of signals (Corresp.)","{\"openalex\":\"W2138548210\",\"doi\":\"10.1109/tit.1974.1055219\"}","2026-05-14T08:54:57.378040232","2026-05-21T12:00:15.185772645","10.1109/tit.1974.1055219","W2138548210","Some communication systems require sets of signals with impulse-like autocorrelation functions and small cross correlation. There is considerable literature on signals with impulse-like autocorrelation functions hut little on sets of signals with small cross correlation. A possible reason is that designers put too severe a restriction on cross correlation magnitudes. 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L. R. Welch 人物

L. R. Welch · 相关事件