Coordinate-Ordering-Free Upper Bounds for Linear Insertion-Deletion Codes
نویسندگان
چکیده
In this paper we prove several coordinate-ordering-free upper bounds on the insdel distances of linear codes. Our are stronger than some previous known bounds. We apply these to AGFC codes from cyclic and one algebraic-geometric code with any rearrangement coordinate positions. A strong bound Reed-Muller special ordering is also given.
منابع مشابه
Insertion and Deletion for Involution Codes
This paper introduces a generalization of the operation of catenation: u[k]lv, the left-k-insertion, is the set of all words obtained by inserting v into u in positions that are at most k letters away from the left extremity of the word u. We define k-suffix codes using the left-kinsertion operation and extend the concept of k-prefix and k-suffix codes to involution k-prefix and involution k-su...
متن کاملCapacity upper bounds for deletion-type channels
We develop a systematic approach, based on convex programming and real analysis, for obtaining upper bounds on the capacity of the binary deletion channel and, more generally, channels with i.i.d. insertions and deletions. Other than the classical deletion channel, we give a special attention to the Poisson-repeat channel introduced by Mitzenmacher and Drinea (IEEE Transactions on Information T...
متن کاملNew Upper Bounds for Some Spherical Codes
The maximal cardinality of a code W on the unit sphere in n dimensions with (x, y) ≤ s whenever x, y ∈ W, x 6= y, is denoted by A(n, s). We use two methods for obtaining new upper bounds on A(n, s) for some values of n and s. We find new linear programming bounds by suitable polynomials of degrees which are higher than the degrees of the previously known good polynomials due to Levenshtein [11,...
متن کاملNew upper bounds for binary covering codes
Improved upper bounds are presented for K(n, r), the minimum cardinality of a binary code of length n and coveting radius r. The new bounds are obtained by both new and old constructions; in many of these, computer search using simulated annealing and tabu search plays a central role. Some new linear coveting codes are also presented. An updated table of upper bounds on K(n,r), n~<64, r~<12, is...
متن کاملUpper bounds for constant-weight codes
Let ( ) denote the maximum possible number of codewords in an ( ) constant-weight binary code. We improve upon the best known upper bounds on ( ) in numerous instances for 24 and 12, which is the parameter range of existing tables. Most improvements occur for = 8 10 where we reduce the upper bounds in more than half of the unresolved cases. We also extend the existing tables up to 28 and 14. To...
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: IEEE Transactions on Information Theory
سال: 2022
ISSN: ['0018-9448', '1557-9654']
DOI: https://doi.org/10.1109/tit.2022.3167662