On normal and subnormal q-ary codes

The authors extend to the q-ary case the notions of a normal code, a subnormal code, and the amalgamated direct sum construction, in order to investigate problems related to the covering radius of codes. For example, the authors prove that every nonbinary nontrivial perfect code is absubnormal. They...

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Published inIEEE transactions on information theory Vol. 35; no. 6; pp. 1291 - 1295
Main Authors Lobstein, A.C., van Wee, G.J.M.
Format Journal Article
LanguageEnglish
Published New York, NY IEEE 01.11.1989
Institute of Electrical and Electronics Engineers
Subjects
Applied sciences
Coding, codes
Error correction codes
Exact sciences and technology
Galois fields
Hamming distance
Information, signal and communications theory
Linear code
Linear programming
Mathematics
Signal and communications theory
Telecommunications and information theory
Upper bound
Lower bound
Linear programming
Ternary system
Binary code
Code
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Abstract The authors extend to the q-ary case the notions of a normal code, a subnormal code, and the amalgamated direct sum construction, in order to investigate problems related to the covering radius of codes. For example, the authors prove that every nonbinary nontrivial perfect code is absubnormal. They also include some linear-programming lower bounds on ternary codes with covering radius 2 or 3.< >
AbstractList The authors extend to the q-ary case the notions of a normal code, a subnormal code, and the amalgamated direct sum construction, in order to investigate problems related to the covering radius of codes. For example, the authors prove that every nonbinary nontrivial perfect code is absubnormal. They also include some linear-programming lower bounds on ternary codes with covering radius 2 or 3.< >
Author Lobstein, A.C.
van Wee, G.J.M.
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Cites_doi 10.1137/0117123
10.1016/S0021-9800(67)80102-9
10.1109/TIT.1985.1057039
10.1109/18.2632
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10.1016/0097-3165(91)90024-B
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10.1109/TIT.1986.1057227
10.1137/0608050
10.1016/0097-3165(84)90010-4
10.1007/BF01817562
10.1109/18.2644
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Keywords Lower bound
Linear programming
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References ref12
cohen (ref3) 1986
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van wee (ref17) 1988; it 34
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macwilliams (ref14) 1977
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SubjectTerms Applied sciences
Coding, codes
Error correction codes
Exact sciences and technology
Galois fields
Hamming distance
Information, signal and communications theory
Linear code
Linear programming
Mathematics
Signal and communications theory
Telecommunications and information theory
Upper bound
Title On normal and subnormal q-ary codes
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Volume 35
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