Unrestricted codes with the golay parameters are unique
نویسندگان
چکیده
منابع مشابه
Golay Codes
We discuss a specific type of error-control coding using Golay codes. First we introduce the basics of coding. Then we discuss the Golay code in binary form, extended binary form, and ternary form.
متن کاملIntersections of Golay codes with higher order Kerdock codes
Golay codewords are useful for transmission schemes such as OFDM, and [MacWilliams/Sloane] demonstrated that these codewords are bent functions contained in second order Reed-Muller codes. This paper investigates the intersection between these codes and Kerdock-like codes.
متن کاملConstructions of the Golay Codes: A Survey
1.1 Preliminaries A code of length n over the finite field Fq is a subset of V = F n q , and it is linear if it is an Fq-subspace of V . When q = 2 we talk of binary codes and binary linear codes. The weight w(a) of an element a ∈ V is the number of non-zero entries in a. The minimum weight of a linear code C is the smallest number which is a weight of a non-zero element of C. The weight enumer...
متن کاملOn Construction of the (24,12,8) Golay Codes
—Two product array codes are used to construct the (24, 12, 8) binary Golay code through the direct sum operation. This construction provides a systematic way to find proper (8, 4, 4) linear block component codes for generating the Golay code, and it generates and extends previously existing methods that use a similar construction framework. The code constructed is simple to decode.
متن کاملSymbol-by-symbol APP decoding of the Golay code and iterative decoding of concatenated Golay codes
An efficient coset based symbol-by-symbol soft-in/soft-out APP decoding algorithm is presented for the Golay code. Its application in the iterative decoding of concatenated Golay codes is examined.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1975
ISSN: 0012-365X
DOI: 10.1016/0012-365x(75)90047-3