Perfect Codes Correcting a Single Burst of Limited-Magnitude Errors
نویسندگان
چکیده
Motivated by applications to DNA-storage, flash memory, and magnetic recording, we study perfect burst-correcting codes for the limited-magnitude error channel. These are lattices that tile integer grid with appropriate ball. We construct two classes of such correcting a single burst length 2, where each affects corresponding position increasing it one, both cyclic non-cyclic bursts. also present generic construction requires primitive element in finite field specific properties. then show various parameter regimes elements exist, hence, infinitely many exist.
منابع مشابه
Some codes correcting single symmetric errors of limited magnitude
An error model with symmetric errors of limited magnitude is considered. Limited magnitude means that the size of any error is limited by a number smaller (usually much smaller) than the alphabet size. Several constructions of codes correcting single error are given. In some cases, the codes are perfect or quasi-perfect.
متن کاملConstructions for perfect 2-burst-correcting codes
In this correspondence, we present two constructions. In the first construction, we show how to generate perfect linear codes of length 2 , 5, and redundancy , which correct a single burst of length 2. In the second construction, we show how to generate perfect linear codes organized in bytes of length 2 , 5, with redundancy divisible by , which correct a single burst of length 2 within the bytes.
متن کاملCodes of Length 2 Correcting Single Errors of Limited Size
Linear codes over Zq of length 2, correcting single errors of size at most k, are considered. It is determined for which q such codes exists and explicit code constructions are given for those q. One case remains open, namely q = (k + 1)(k + 2), where k + 1 is a prime power. For this case we conjecture that no such codes exist.
متن کاملCodes Correcting Repeated Burst Errors Blockwise
This paper obtains bounds for linear codes which are capable to correct the errors blockwise which occur during the process of transmission. The kind of errors considered are known as repeated burst errors of length b(fixed), introduced by Dass and Garg (2009). An illustration for such kind of codes has also been provided. Mathematics Subject Classification: 94B20, 94B25, 94B65
متن کاملErratum to: Linear covering codes and error-correcting codes for limited-magnitude errors
The expression for ω 2,2,r (2t) in Theorem 9 is misprinted in the original publication of this article. It should have been the same as for ω 2,1,r (2t) in Theorem 11. The correct expression in Theorem 9 will be Theorem 9 For q = 2t where t is odd, we have ω 2,2,r (2t) = 1 2 (2 r − 1)(t r + 1) .
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: 2023
ISSN: ['0018-9448', '1557-9654']
DOI: https://doi.org/10.1109/tit.2022.3213239