Maximum distance&amp;lt;tex&amp;gt;q&amp;lt;/tex&amp;gt;-nary codes

Singleton, Richard C.

doi:10.1109/tit.1964.1053661

Cited by 437 publications

(171 citation statements)

References 2 publications

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“…Equivalence maintains the Hamming distance between codewords but not linearity. A general bound for the size of an (n, M, d) q code is the Singleton bound [1], which states that…”

Section: Introductionmentioning

confidence: 99%

On the Classification of MDS Codes

Kokkala

Krotov

Östergård

2015

IEEE Trans. Inform. Theory

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A q-ary code of length n, size M , and minimum distance d is called an (n, M, d)q code. An (n, q k , n − k + 1)q code is called a maximum distance separable (MDS) code. In this work, some MDS codes over small alphabets are classified. It is shown that every7} is equivalent to a linear code with the same parameters. This implies that the (6, 5 4 , 3)5 code and the (n, 7 n−2 , 3)7 MDS codes for n ∈ {6, 7, 8} are unique. The classification of one-errorcorrecting 8-ary MDS codes is also finished; there are 14, 8, 4, and 4 equivalence classes of (n, 8 n−2 , 3)8 codes for n = 6, 7, 8, 9, respectively. One of the equivalence classes of perfect (9,8 7 , 3)8 codes corresponds to the Hamming code and the other three are nonlinear codes for which there exists no previously known construction.

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“…Equivalence maintains the Hamming distance between codewords but not linearity. A general bound for the size of an (n, M, d) q code is the Singleton bound [1], which states that…”

Section: Introductionmentioning

confidence: 99%

On the Classification of MDS Codes

Kokkala

Krotov

Östergård

2015

IEEE Trans. Inform. Theory

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“…This principle extends to any n > k by using, e.g., erasure codes that are maximum distance separable cf. [38].…”

Section: Thus Using Any Twoỹ T (I)ỹ T (J) I = J Both Y T (1) and Ymentioning

confidence: 99%

Multiple descriptions for packetized predictive control

Østergaard

Quevedo

2016

EURASIP J. Adv. Signal Process.

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In this paper, we propose to use multiple descriptions (MDs) to achieve a high degree of robustness towards random packet delays and erasures in networked control systems. In particular, we consider the scenario, where a data-rate limited channel is located between the controller and the plant input. This forward channel also introduces random delays and dropouts. The feedback channel from the plant output to the controller is assumed noiseless. We show how to design MDs for packetized predicted control (PPC) in order to enhance the robustness. In the proposed scheme, a quantized control vector with future tentative control signals is transmitted to the plant at each discrete time instant. This control vector is then transformed into M redundant descriptions (packets) such that when receiving any 1 ≤ J ≤ M packets, the current control signal as well as J − 1 future control signals can be reliably reconstructed at the plant side. For the particular case of LTI plant models and i.i.d. channels, we show that the overall system forms a Markov jump linear system. We provide conditions for mean square stability and derive upper bounds on the operational bit rate of the quantizer to guarantee a desired performance level. Simulations reveal that a significant gain over conventional PPC can be achieved when combining PPC with suitably designed MDs.

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“…The Singleton bound [25] in coding theory implies that the highest branch number possible is r + 1. An r × r matrix P having such a branch number is called an MDS (Maximum Distance Separable) matrix and is frequently utilized in cryptography.…”

Section: Branch Numbers and Mds Matricesmentioning

confidence: 99%

Known-Key Distinguishers on 11-Round Feistel and Collision Attacks on Its Hashing Modes

Sasaki

Yasuda

2011

Fast Software Encryption

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Abstract. We present new attacks on the Feistel network, where each round function consists of a subkey XOR, S-boxes, and then a linear transformation (i.e., an SP round function). Our techniques are based largely on what they call the rebound attacks. As a result, our attacks work most effectively when the S-boxes have a "good" differential property (like the inverse function x → x −1 in the finite field) and when the linear transformation has an "optimal" branch number (i.e., a maximum distance separable matrix). We first describe known-key distinguishers on such Feistel block ciphers of up to 11 rounds, increasing significantly the number of rounds from previous work. We then apply our distinguishers to the Matyas-Meyer-Oseas and Miyaguchi-Preneel modes in which the Feistel ciphers are used, obtaining collision and half-collision attacks on these hash functions.

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Maximum distance<tex>q</tex>-nary codes

Cited by 437 publications

References 2 publications

On the Classification of MDS Codes

On the Classification of MDS Codes

Multiple descriptions for packetized predictive control

Known-Key Distinguishers on 11-Round Feistel and Collision Attacks on Its Hashing Modes

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