Generalized Gray map and a class of p-ary nonlinear codes
نویسندگان
چکیده
منابع مشابه
Balancing Cyclic R-ary Gray Codes II
New cyclic n-digit Gray codes are constructed over {0, 1, . . . , R − 1} for all R ≥ 2, n ≥ 3. These codes have the property that the distribution of digit changes (transition counts) between two successive elements is close to uniform. For R = 2, the construction and proof are simpler than earlier balanced cyclic binary Gray codes. For R ≥ 3 and n ≥ 2, every transition count is within 2 of the...
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New cyclic n-digit Gray codes are constructed over {0, 1, . . . , R − 1} for all R,n ≥ 2. These codes have the property that the distribution of the digit changes (transition counts) is close to uniform: For every n ≥ 2, the number of occurrences of each digit in the n-digit codes is within R-1 of the average Rn/n, and for the 2-digit codes every transition count is either bR2/2c or dR2/2e.
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An efficient algorithm for enumerating a sequence of all elements in (Zn) k in a special order is presented. The sequence enumerated is called the (n,k)-Gray code. It has the property that each pair of adjacent elements differs in only one digit and the difference is either +1 or −1. This sequence can be efficiently applied to calculation of the weight polynomial of a group code. We also show t...
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Let m, k be positive integers such that m gcd(m,k) ≥ 3, p be an odd prime and π be a primitive element of Fpm. Let h1(x) and h2(x) be the minimal polynomials of −π−1 and π pk+1 2 over Fp, respectively. In the case of odd m gcd(m,k) , when k is even, gcd(m,k) is odd or when k gcd(m,k) is odd, Zhou et al. in [25] obtained the weight distribution of a class of cyclic codes C over Fp with parity-ch...
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Generalizing a theorem of McEliece, one obtains the highest power of p dividing all weights of a p-ary Abelian code, as a function of the set of nonzeros of that code. 1. Introduetion The important theorem of McEliece 7.8) on the weights of cyclic codes can be stated as follows. Let C be a cyclic code, of length n:;i: 0 (mod p), over the prime field GF(y) and let 'I' be the least positive integ...
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ژورنال
عنوان ژورنال: Finite Fields and Their Applications
سال: 2015
ISSN: 1071-5797
DOI: 10.1016/j.ffa.2015.06.006