How Many Weights Can a Quasi-Cyclic Code Have?
نویسندگان
چکیده
منابع مشابه
How many weights can a linear code have?
We study the combinatorial function L(k, q), the maximum number of nonzero weights a linear code of dimension k over Fq can have. We determine it completely for q = 2, and for k = 2, and provide upper and lower bounds in the general case when both k and q are ≥ 3. A refinement L(n, k, q), as well as nonlinear analogues N(M, q) and N(n,M, q), are also introduced and studied.
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We prove a complex polynomial of degree n has at most ⌈n/2⌉ attractive fixed points lying on a line. We also consider the general case.
متن کاملQuasi-Cyclic Complementary Dual Code
LCD codes are linear codes that intersect with their dual trivially. Quasi-cyclic codes that are LCD are characterized and studied by using their concatenated structure. Some asymptotic results are derived. Hermitian LCD codes are introduced to that end and their cyclic subclass is characterized. Constructions of QCCD codes from codes over larger alphabets are given.
متن کاملHow many runs can a string contain?
Given a string x = x[1..n], a repetition of period p in x is a substring ur = x[i+1..i+rp], p = |u|, r ≥ 2, where neither u = x[i+1..i+p] nor x[i+1..i+(r+1)p+1] is a repetition. The maximum number of repetitions in any string x is well known to be Θ(n log n). A run or maximal periodicity of period p in x is a substring urt = x[i+1..i+rp+ |t|] of x, where ur is a repetition, t a proper prefix of...
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All our words (strings) are over a fixed alphabet. A square is a subword of the form uu=u, where u is a nonempty word. Two squares are distinct if they are of different shape, not just translates of each other. A word u is primitive if u cannot be written in the form u=v j for some j 2. A square u with u primitive is primitive rooted. Let M(n) denote the maximum number of distinct squares, P(n)...
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ژورنال
عنوان ژورنال: IEEE Transactions on Information Theory
سال: 2020
ISSN: 0018-9448,1557-9654
DOI: 10.1109/tit.2020.3001591