LYM-type inequalities for tEC/AUED codes

Some LYM-type inequalities are introduced to obtain a relationship between the parameters of t-error correcting/all unidirectional error-detecting codes of length n. As an application of these inequalities, new lower bounds on the redundancies of systematic tEC/AUED codes are derived and an extensive table is given. >

[1]  Dhiraj K. Pradhan,et al.  Optimal Unidirectional Error Detecting/Correcting Codes , 1982, IEEE Transactions on Computers.

[2]  Dhiraj K. Pradhan,et al.  A New Class of Error-Correcting/Detecting Codes for Fault-Tolerant Computer Applications , 1980, IEEE Transactions on Computers.

[3]  Jehoshua Bruck,et al.  Some new EC/AUED codes , 1989, [1989] The Nineteenth International Symposium on Fault-Tolerant Computing. Digest of Papers.

[4]  Dhiraj K. Pradhan,et al.  Error-Correcting Codes and Self-Checking Circuits , 1980, Computer.

[5]  D. Lubell A Short Proof of Sperner’s Lemma , 1966 .

[6]  Rudolf Ahlswede,et al.  On cloud-antichains and related configurations , 1990, Discret. Math..

[7]  Henk C. A. van Tilborg,et al.  Constructions and bounds for systematic t EC/AUED codes , 1990, IEEE Trans. Inf. Theory.

[8]  Robert W. Cook,et al.  Design of a Self-Checking Microprogram Control , 1973, IEEE Transactions on Computers.

[9]  William T. Trotter,et al.  A Sperner Theorem on Unrelated Chains of Subsets , 1984, J. Comb. Theory, Ser. A.

[10]  L Chen A NOTE ON SYSTEMATIC tEC-MUED CODE , 1984 .

[11]  L. D. Meshalkin Generalization of Sperner’s Theorem on the Number of Subsets of a Finite Set , 1963 .

[12]  D. Kleitman,et al.  Proof techniques in the theory of finite sets , 1978 .

[13]  John F. Wakerly,et al.  Detection of Unidirectional Multiple Errors Using Low-Cost Arithmetic Codes , 1975, IEEE Transactions on Computers.

[14]  Koichiro Yamamoto Logarithmic order of free distributive lattice , 1954 .

[15]  Rudolf Ahlswede,et al.  An identity in combinatorial extremal theory , 1990 .

[16]  Dimitris Nikolos,et al.  Systematic t-Error Correcting/All Unidirectional Error Detecting Codes , 1984, IEEE Transactions on Computers.

[17]  Victor K.-W. Wei A connection between a convex programming problem and the LYM property on perfect graphs , 1988, J. Graph Theory.

[18]  Clyde L. Monma,et al.  Convex Resource Allocation Problems on Directed Acyclic Graphs: Duality, Complexity, Special Cases, and Extensions , 1990, Math. Oper. Res..

[19]  Mario Blaum,et al.  On t-Error Correcting/All Unidirectional Error Detecting Codes , 1989, IEEE Trans. Computers.

[20]  Bella Bose,et al.  Theory of Unidirectional Error Correcting/Detecting Codes , 1978, IEEE Transactions on Computers.