Optimal p-ary cyclic codes with two zeros
نویسندگان
چکیده
As a subclass of linear codes, cyclic codes have efficient encoding and decoding algorithms, so they are widely used in many areas such as consumer electronics, data storage systems communication systems. In this paper, we give general construction optimal p-ary which leads to three explicit constructions. addition, another class presented.
منابع مشابه
The weight distributions of two classes of p-ary cyclic codes with few weights
Cyclic codes have attracted a lot of research interest for decades as they have efficient encoding and decoding algorithms. In this paper, for an odd prime p, the weight distributions of two classes of p-ary cyclic codes are completely determined. We show that both codes have at most five nonzero weights.
متن کاملOn the weight distribution of the duals of irreducible cyclic codes, cyclic codes with two zeros and hyper-Kloosterman codes
This paper considers the weight distributions of binary cyclic codes with one or two zeros and hyper-Kloosterman codes. The results on value distributions of certain monomial exponential sums and connections between exponential sums and Kloosterman sums are applied together with the Pless power moment identity in these conciderations. Explicit formulae for the number of low-weight codewords are...
متن کاملBalancing 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...
متن کاملBalancing Cyclic R-ary Gray Codes
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.
متن کاملNew bounds on D-ary optimal codes
We propose a simple method that, given a symbol distribution, yields upper and lower bounds on the average code length of a D-ary optimal code over that distribution. Thanks to its simplicity, the method permits deriving analytical bounds for families of parametric distributions. We demonstrate this by obtaining new bounds, much better than the existing ones, for Zipf and exponential distributi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Applicable Algebra in Engineering, Communication and Computing
سال: 2021
ISSN: ['1432-0622', '0938-1279']
DOI: https://doi.org/10.1007/s00200-021-00489-5