A computing device (100), comprising a memory (240) and a controller (210), wherein said controller (210) is configured to compress a file (410) by transforming at least a portion of said file (410) to a number (X) and transforming the number (X) to an exponent vector (exp) comprising at least one exponent, wherein each exponent corresponds to a base in a base vector (base).

Text can be encoded into DNA sequences. Each word from a document or other text sample can be encoded in a DNA sequence or DNA sequences and the DNA sequences can be stored for later retrieval. The DNA sequences can be stored digitally, or actual DNA molecules containing the sequences can be synthesized and stored. In one example, the encoding technique makes use of a polynomial function to transform words based on the Latin alphabet into k-mer DNA sequences of length k. Because the whole bits required for the DNA sequences are smaller than the actual strings of words, storing documents using DNA sequences may compress the documents relative to storing the same documents using other techniques. In at least one example, the mapping between words and DNA sequences is one-to-one and the collision ratio for the encoding is low.

Entropy agnostic data encoding includes: receiving, by an encoder, input data including a bit string; generating a plurality of candidate codewords, including encoding the input data bit string with a plurality of binary vectors, wherein the plurality of binary vectors includes a set of deterministic biased binary vectors and a set of random binary vectors; selecting, in dependence upon a predefined criteria, one of the plurality of candidate codewords; and transmitting the selected candidate codeword to a decoder.

Methods of encoding and decoding data are described wherein the encoding method comprises: receiving a data file and dividing the data file or data stream into one or more data blocks, each data block having a predetermined size N and comprising a sequence of data units, e.g. byte values; and, iteratively encoding the data file into a data key based on a first permutation function and a first dictionary of permutation indices, preferably the encoded data file having a total size that is equal to or smaller than the original data file and preferably the data key having a size that is equal to or smaller than size of a data block. Iteratively encoding the data file comprises one or more encoding iterations, wherein each encoding iteration includes: determining a first permutation index defining a permutation to generate the first input data block from a first ordered data block, the generating including providing at least the first input data block to an input of the first permutation function, and the first ordered data block being obtainable by ordering the first input data block; determining a first permutation dictionary index representing a location in the first dictionary in which the first permutation index is stored; generating a first frequency data block defining the number of occurrences for each potential data value in the input data block, preferably determining the number of occurrences for each potential data value in the input data block and ordering the determined occurrences in a sequence of values in a hierarchical order, e.g. increasing or decreasing order of the data value; processing the frequency data block; and determining an encoded data block, the encoded data block comprising the first permutation dictionary index and the processed frequency data block. The encoding method further comprises outputting the data key comprising the one or more encoded data blocks and, optionally, iteration information.

Decomposing a value range of the respective syntax elements into a sequence of n partitions with coding the components of z laying within the respective partitions separately with at least one by VLC coding and with at least one by PIPE or entropy coding is used to greatly increase the compression efficiency at a moderate coding overhead since the coding scheme used may be better adapted to the syntax element statistics. Accordingly, syntax elements are decomposed into a respective number n of source symbols s.sub.i with i=1 . . . n, the respective number n of source symbols depending on as to which of a sequence of n partitions into which a value range of the respective syntax elements is sub-divided, a value z of the respective syntax elements falls into, so that a sum of values of the respective number of source symbols s.sub.i yields z, and, if n>1, for all i=1 . . . n−1, the value of s.sub.i corresponds to a range of the i.sup.th partition.

The present disclosure relates to a computer language and code for software application development, data compression, and use with conventional, optical, hybrid electro-optical and quantum computers.

In the data compression method, a raw data block in raw data is processed based on a compression algorithm to obtain a standard compressed data block that has a length of L2 and that corresponds to the raw data block, and the raw data is further compressed into one or more standard compressed data blocks that each have the length of L2 and that are to be decompressed in parallel by a decompression apparatus, where the decompression apparatus includes a plurality of decompression engines, and each decompression engine is capable of decompressing one standard compressed data block within one processing cycle. According to the data compression method, a standard compressed data block with a fixed length can be obtained through compression.

Decomposing a value range of the respective syntax elements into a sequence of n partitions with coding the components of z laying within the respective partitions separately with at least one by VLC coding and with at least one by PIPE or entropy coding is used to greatly increase the compression efficiency at a moderate coding overhead since the coding scheme used may be better adapted to the syntax element statistics. Accordingly, syntax elements are decomposed into a respective number n of source symbols s.sub.i with i=1 . . . n, the respective number n of source symbols depending on as to which of a sequence of n partitions into which a value range of the respective syntax elements is sub-divided, a value z of the respective syntax elements falls into, so that a sum of values of the respective number of source symbols s.sub.i yields z, and, if n>1, for all i=1 . . . n−1, the value of s.sub.i corresponds to a range of the i.sup.th partition.

A digital signature method includes: obtaining a to-be-transmitted file, a private key and first compressed data, the first compressed data being obtained through compressing a symmetric tensor, the private key including a first invertible matrix; generating L pieces of second compressed data corresponding to L second symmetric tensors in accordance with the first invertible matrix and the first compressed data; creating a Hash value of a root node in a Hash tree in accordance with L pieces of created data, the L pieces of created data being the L pieces of second compressed data or the L second symmetric tensors; and generating signature information about the to-be-transmitted file for the first electronic device in accordance with the first character string, the first invertible matrix, the second invertible matrix, the L pieces of second compressed data and the Hash value of the root node in the Hash tree.

A system transmits a target data file as a set of mathematical functions and data values representative of the target data file to a receiver, the system comprising at least one hardware processor and memory storing computer instructions, the computer instructions when executed by the at least one hardware processor configured to cause the system to identify a target bit pattern of a target data file; generate a set of mathematical functions and data values operative to generate the target bit pattern; and transmit the set of mathematical functions and data values to a receiver, which can use the set of mathematical functions and data values to generate the target data file.