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The linear independence of the columns of a generator matrix of an MDS code permits a construction of MDS codes from objects in finite projective geometry. Let P G ( N , q ) {\displaystyle PG(N,q)} be the finite projective space of (geometric) dimension N {\displaystyle N} over the finite field F q {\displaystyle \mathbb {F} _{q}} .
1944 – World War II: A combined Canadian–Polish force captured the town of Falaise, France, in the final offensive of the Battle of Normandy. 2007 – BioShock was released in North America, becoming a critical success and a demonstration of video games as an art form .
Convolutional code with any code rate can be designed based on polynomial selection; [15] however, in practice, a puncturing procedure is often used to achieve the required code rate. Puncturing is a technique used to make a m/n rate code from a "basic" low-rate (e.g., 1/n) code. It is achieved by deleting of some bits in the encoder output.
For practical purposes, parity-check matrix of a binary Goppa code is usually converted to a more computer-friendly binary form by a trace construction, that converts the -by-matrix over () to a -by-binary matrix by writing polynomial coefficients of () elements on successive rows.
As of the 2020s, many anime fans and followers use social media platforms and other sites like YouTube, Twitch, [206] Fandom, [207] Facebook, Reddit, [208] Discord, [209] Tumblr, [210] 4chan, TikTok and Twitter [211] [212] with online communities and databases such as IMDb, MyAnimeList to discuss anime, manga and track their progress watching ...
Area code 619 is shown in red. Area codes 619 and 858 are telephone area codes in the North American Numbering Plan (NANP) for most of San Diego County in the U.S. state of California. Area code 619 was created by a split of area code 714 in 1982. In 1999, a part of the 619 numbering plan area was
The Morse code, as specified in the current international standard, International Morse Code Recommendation, ITU-R M.1677-1, [1] was derived from a much-improved proposal by Friedrich Gerke in 1848 that became known as the "Hamburg alphabet", its only real defect being the use of an excessively long code ( and later the equal duration code ...
The parity-check matrix H of a Hamming code is constructed by listing all columns of length m that are pair-wise independent. Thus H is a matrix whose left side is all of the nonzero n-tuples where order of the n-tuples in the columns of matrix does not matter.