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If the block code is a linear block code, then the square brackets in the notation <math>[n,k,d]_q</math> are used to represent that fact. |
If the block code is a linear block code, then the square brackets in the notation <math>[n,k,d]_q</math> are used to represent that fact. |
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For binary codes with <math>q=2</math>, the index is sometimes dropped. |
For binary codes with <math>q=2</math>, the index is sometimes dropped. |
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For [[maximum distance separable code]]s, the distance is always <math>d=n-k+1</math>, |
For [[maximum distance separable code]]s, the distance is always <math>d=n-k+1</math>, and sometimes the precise distance is not known, non-trivial to prove or state, or not needed. In such cases, the <math>d</math>-component may be missing. |
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Sometimes, especially for non-block codes, the notation <math>(n,M,d)_q</math> is used for codes that contain <math>M</math> codewords of length <math>n</math>. For block codes with messages of length <math>k</math> over an alphabet of size <math>q</math>, this number would be <math>M=q^k</math>. |
Sometimes, especially for non-block codes, the notation <math>(n,M,d)_q</math> is used for codes that contain <math>M</math> codewords of length <math>n</math>. For block codes with messages of length <math>k</math> over an alphabet of size <math>q</math>, this number would be <math>M=q^k</math>. |
Copy and paste: – — ° ′ ″ ≈ ≠ ≤ ≥ ± − × ÷ ← → · § Cite your sources: <ref></ref>
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Symbols: ~ | ¡ ¿ † ‡ ↔ ↑ ↓ • ¶ # ∞ ‹› «» ¤ ₳ ฿ ₵ ¢ ₡ ₢ $ ₫ ₯ € ₠ ₣ ƒ ₴ ₭ ₤ ℳ ₥ ₦ № ₧ ₰ £ ៛ ₨ ₪ ৳ ₮ ₩ ¥ ♠ ♣ ♥ ♦ 𝄫 ♭ ♮ ♯ 𝄪 © ® ™
Latin: A a Á á À à  â Ä ä Ǎ ǎ Ă ă Ā ā à ã Å å Ą ą Æ æ Ǣ ǣ B b C c Ć ć Ċ ċ Ĉ ĉ Č č Ç ç D d Ď ď Đ đ Ḍ ḍ Ð ð E e É é È è Ė ė Ê ê Ë ë Ě ě Ĕ ĕ Ē ē Ẽ ẽ Ę ę Ẹ ẹ Ɛ ɛ Ǝ ǝ Ə ə F f G g Ġ ġ Ĝ ĝ Ğ ğ Ģ ģ H h Ĥ ĥ Ħ ħ Ḥ ḥ I i İ ı Í í Ì ì Î î Ï ï Ǐ ǐ Ĭ ĭ Ī ī Ĩ ĩ Į į Ị ị J j Ĵ ĵ K k Ķ ķ L l Ĺ ĺ Ŀ ŀ Ľ ľ Ļ ļ Ł ł Ḷ ḷ Ḹ ḹ M m Ṃ ṃ N n Ń ń Ň ň Ñ ñ Ņ ņ Ṇ ṇ Ŋ ŋ O o Ó ó Ò ò Ô ô Ö ö Ǒ ǒ Ŏ ŏ Ō ō Õ õ Ǫ ǫ Ọ ọ Ő ő Ø ø Œ œ Ɔ ɔ P p Q q R r Ŕ ŕ Ř ř Ŗ ŗ Ṛ ṛ Ṝ ṝ S s Ś ś Ŝ ŝ Š š Ş ş Ș ș Ṣ ṣ ß T t Ť ť Ţ ţ Ț ț Ṭ ṭ Þ þ U u Ú ú Ù ù Û û Ü ü Ǔ ǔ Ŭ ŭ Ū ū Ũ ũ Ů ů Ų ų Ụ ụ Ű ű Ǘ ǘ Ǜ ǜ Ǚ ǚ Ǖ ǖ V v W w Ŵ ŵ X x Y y Ý ý Ŷ ŷ Ÿ ÿ Ỹ ỹ Ȳ ȳ Z z Ź ź Ż ż Ž ž ß Ð ð Þ þ Ŋ ŋ Ə ə
Greek: Ά ά Έ έ Ή ή Ί ί Ό ό Ύ ύ Ώ ώ Α α Β β Γ γ Δ δ Ε ε Ζ ζ Η η Θ θ Ι ι Κ κ Λ λ Μ μ Ν ν Ξ ξ Ο ο Π π Ρ ρ Σ σ ς Τ τ Υ υ Φ φ Χ χ Ψ ψ Ω ω {{Polytonic|}}
Cyrillic: А а Б б В в Г г Ґ ґ Ѓ ѓ Д д Ђ ђ Е е Ё ё Є є Ж ж З з Ѕ ѕ И и І і Ї ї Й й Ј ј К к Ќ ќ Л л Љ љ М м Н н Њ њ О о П п Р р С с Т т Ћ ћ У у Ў ў Ф ф Х х Ц ц Ч ч Џ џ Ш ш Щ щ Ъ ъ Ы ы Ь ь Э э Ю ю Я я ́
IPA: t̪ d̪ ʈ ɖ ɟ ɡ ɢ ʡ ʔ ɸ β θ ð ʃ ʒ ɕ ʑ ʂ ʐ ç ʝ ɣ χ ʁ ħ ʕ ʜ ʢ ɦ ɱ ɳ ɲ ŋ ɴ ʋ ɹ ɻ ɰ ʙ ⱱ ʀ ɾ ɽ ɫ ɬ ɮ ɺ ɭ ʎ ʟ ɥ ʍ ɧ ʼ ɓ ɗ ʄ ɠ ʛ ʘ ǀ ǃ ǂ ǁ ɨ ʉ ɯ ɪ ʏ ʊ ø ɘ ɵ ɤ ə ɚ ɛ œ ɜ ɝ ɞ ʌ ɔ æ ɐ ɶ ɑ ɒ ʰ ʱ ʷ ʲ ˠ ˤ ⁿ ˡ ˈ ˌ ː ˑ ̪ {{IPA|}}
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