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Chapter 5 studies cyclic codes and Chapter 6 studies a special case of cyclic codes, the quadratic residue codes. Chapter 7 returns to BCH codes. [1] [6] After these discussions of specific codes, the next chapter concerns enumerator polynomials, including the MacWilliams identities, Pless's own power moment identities, and the Gleason ...
where v 1, v 2, ..., v k are in S, and a 1, a 2, ..., a k are in F form a linear subspace called the span of S. The span of S is also the intersection of all linear subspaces containing S . In other words, it is the smallest (for the inclusion relation) linear subspace containing S .
Matthew 5:9 reads: "Blessed are the peacemakers, for they will be called children of God." [7] Here, the Greek word huioi is translated "children" rather than "sons" as found in other modern English translations such as the Revised Standard Version, [8] New American Standard Bible, [9] New King James Version, [10] and the Amplified Bible. [11]
The New International Version (NIV) is a translation of the Bible into contemporary English. Published by Biblica, the complete NIV was released on October 27, 1978 [6] with a minor revision in 1984 and a major revision in 2011. The NIV relies on recently-published critical editions of the original Hebrew, Aramaic, and Greek texts. [1] [2]
The NIV Study Bible is a study Bible originally published by Zondervan in 1985 that uses the New International Version (NIV). Revisions include one in 1995, a full revision in 2002, an update in October 2008 for the 30th anniversary of the NIV, another update in 2011 (with the text updated to the 2011 edition of the NIV), and a fully revised update in 2020 named "Fully Revised Edition". [1]
Bible Gateway's engagement features include the ability to display a single Bible verse in many English Bible translations, the ability to display and compare up to five Bible translations side by side at once, its daily Blog, more than 60 email devotions, Bible reading plans and verses-of-the-day, a free mobile app, audio Bibles, video ...
As recently as 2019, the Android version of the app was requiring access to all the users contact information (their address book) and even the users GPS location. [ 13 ] [ 14 ] YouVersion has updated their privacy policies as of April 2, 2022.
Robert Estienne (Robert Stephanus) was the first to number the verses within each chapter, his verse numbers entering printed editions in 1551 (New Testament) and 1553 (Hebrew Bible). [24] Several modern publications of the Bible have eliminated numbering of chapters and verses. Biblica published such a version of the NIV in 2007 and