B-symbol Distance Distribution of Repeated-root Cyclic Codes
نویسندگان
چکیده
Symbol-pair codes, introduced by Cassuto and Blaum [1], have been raised for symbol-pair read channels. This new idea is motivated by the limitations of the reading process in high-density data storage technologies. Yaakobi et al. [8] introduced codes for b-symbol read channels, where the read operation is performed as a consecutive sequence of b > 2 symbols. In this paper, we come up with a method to compute the b-symbol-pair distance of two n-tuples, where n is a positive integer. Also, we deal with the b-symbol-pair distances of some kind of cyclic codes of length p over Fpm .
منابع مشابه
The symbol-pair distance distribution of repeated-root cyclic codes over $\mathbb{F}_{p^m}$
Abstract: Symbol-pair codes are proposed to protect against pair errors in symbol-pair read channels. One of the most important task in symbol-pair coding theory is to determine the minimum pair-distance of symbol-pair codes. In this paper, we investigate the symbol-pair distances of cyclic codes of length p over Fpm . The exact symbol-pair distances of all cyclic codes of such length are deter...
متن کاملOn Repeated-root Cyclic Codes
A parity-check matrix for a q -ary repeated-root cyclic code is derived using the Hasse derivative. Then the min imum distance of a q-ary repeated-root cyclic code C is expressecin terms of the min imum distance of a certain simple-root cyclic code C that is determined by C. With the help of this result, several binary repeated-root cyclic codes of lengths up to n = 62 are shown to contain the ...
متن کاملSquaring Construction for Repeated-Root Cyclic Codes
We considered repeated-root cyclic codes whose block length is divisible by the characteristic of the underlying field. Cyclic self dual codes are also the repeated root cyclic codes. It is known about the one-level squaring construction for binary repeated root cyclic codes. In this correspondence, we introduced of two level squaring construction for binary repeated root cyclic codes of length...
متن کاملRepeated-root cyclic and negacyclic codes over a finite chain ring
We show that repeated-root cyclic codes over a finite chain ring are in general not principally generated. Repeated-root negacyclic codes are principally generated if the ring is a Galois ring with characteristic a power of 2. For any other finite chain ring they are in general not principally generated. We also prove results on the structure, cardinality and Hamming distance of repeated-root c...
متن کاملRepeated-root cyclic and negacyclic codes over a nite chain ring
We show that repeated-root cyclic codes over a finite chain ring are in general not principally generated. Repeated-root negacyclic codes are principally generated if the ring is a Galois ring with characteristic a power of 2. For any other finite chain ring they are in general not principally generated. We also prove results on the structure, cardinality and Hamming distance of repeated-root c...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- CoRR
دوره abs/1704.03311 شماره
صفحات -
تاریخ انتشار 2017