On the symbol-pair distance of some classes of repeated-root constacyclic codes over Galois ring

Author(s):  
Hai Q. Dinh ◽  
Narendra Kumar ◽  
Abhay Kumar Singh ◽  
Manoj Kumar Singh ◽  
Indivar Gupta ◽  
...  
2021 ◽  
Vol 28 (04) ◽  
pp. 581-600
Author(s):  
Hai Q. Dinh ◽  
Hualu Liu ◽  
Roengchai Tansuchat ◽  
Thang M. Vo

Negacyclic codes of length [Formula: see text] over the Galois ring [Formula: see text] are linearly ordered under set-theoretic inclusion, i.e., they are the ideals [Formula: see text], [Formula: see text], of the chain ring [Formula: see text]. This structure is used to obtain the symbol-pair distances of all such negacyclic codes. Among others, for the special case when the alphabet is the finite field [Formula: see text] (i.e., [Formula: see text]), the symbol-pair distance distribution of constacyclic codes over [Formula: see text] verifies the Singleton bound for such symbol-pair codes, and provides all maximum distance separable symbol-pair constacyclic codes of length [Formula: see text] over [Formula: see text].


2018 ◽  
Vol 10 (03) ◽  
pp. 1850036 ◽  
Author(s):  
Anuradha Sharma ◽  
Tania Sidana

Let [Formula: see text] be a prime, [Formula: see text] be a positive integer, and let GR[Formula: see text] be the Galois ring of characteristic [Formula: see text] and cardinality [Formula: see text]. In this paper, all repeated-root constacyclic codes of arbitrary lengths over GR[Formula: see text] their sizes and their dual codes are determined. As an application, some isodual constacyclic codes over GR[Formula: see text] are also listed. To illustrate the results, all cyclic and negacyclic codes of length 10 over [Formula: see text] are obtained.


2014 ◽  
Vol 35 (5) ◽  
pp. 1044-1048 ◽  
Author(s):  
Ping Li ◽  
Shi-xin Zhu ◽  
Xiao-shan Kai
Keyword(s):  

Filomat ◽  
2019 ◽  
Vol 33 (8) ◽  
pp. 2237-2248 ◽  
Author(s):  
Habibul Islam ◽  
Om Prakash

In this paper, we study (1 + 2u + 2v)-constacyclic and skew (1 + 2u + 2v)-constacyclic codes over the ring Z4 + uZ4 + vZ4 + uvZ4 where u2 = v2 = 0,uv = vu. We define some new Gray maps and show that the Gray images of (1 + 2u + 2v)-constacyclic and skew (1 + 2u + 2v)-constacyclic codes are cyclic, quasi-cyclic and permutation equivalent to quasi-cyclic codes over Z4. Further, we determine the structure of (1 + 2u + 2v)-constacyclic codes of odd length n.


Author(s):  
Xiaojing Chen ◽  
Shixin Zhu ◽  
Wan Jiang ◽  
Gaojun Luo

2020 ◽  
pp. 1-1
Author(s):  
Wei Zhao ◽  
Shenghao Yang ◽  
Kenneth W. Shum ◽  
Xilin Tang
Keyword(s):  

2021 ◽  
Vol 11 (8) ◽  
pp. 3330
Author(s):  
Pietro Nannipieri ◽  
Stefano Di Matteo ◽  
Luca Baldanzi ◽  
Luca Crocetti ◽  
Jacopo Belli ◽  
...  

Random numbers are widely employed in cryptography and security applications. If the generation process is weak, the whole chain of security can be compromised: these weaknesses could be exploited by an attacker to retrieve the information, breaking even the most robust implementation of a cipher. Due to their intrinsic close relationship with analogue parameters of the circuit, True Random Number Generators are usually tailored on specific silicon technology and are not easily scalable on programmable hardware, without affecting their entropy. On the other hand, programmable hardware and programmable System on Chip are gaining large adoption rate, also in security critical application, where high quality random number generation is mandatory. The work presented herein describes the design and the validation of a digital True Random Number Generator for cryptographically secure applications on Field Programmable Gate Array. After a preliminary study of literature and standards specifying requirements for random number generation, the design flow is illustrated, from specifications definition to the synthesis phase. Several solutions have been studied to assess their performances on a Field Programmable Gate Array device, with the aim to select the highest performance architecture. The proposed designs have been tested and validated, employing official test suites released by NIST standardization body, assessing the independence from the place and route and the randomness degree of the generated output. An architecture derived from the Fibonacci-Galois Ring Oscillator has been selected and synthesized on Intel Stratix IV, supporting throughput up to 400 Mbps. The achieved entropy in the best configuration is greater than 0.995.


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